Exactly how old IS The Doctor? The question is not as straightforward as it seems. This piece from the Wikipedia entry for The Doctor goes some way to explaining the problem.

The Doctor's Age

The Doctor's age has been stated (or estimated) in several stories. In the serial The Tomb of the Cybermen, the Second Doctor told Victoria that he was around 450 years old. The Second Doctor was also seen to carry around a 500-year diary in which he kept notes. The Third Doctor implied that he had a lifetime that covered several thousand years, but he may have been referring to the time span he had seen on his travels rather than actually lived through, or perhaps his own life expectancy.

By the time of The Brain of Morbius, the Fourth Doctor was stated to be 749 years old ("something like 750 years" in the prior Pyramids of Mars). In The Ribos Operation, the first Romana said the Doctor was 759 years old and had been piloting the TARDIS for 523 years, making him 236 when he first "borrowed" it. In Revelation of the Daleks the Sixth Doctor was 900 years old, and in Time and the Rani, the Seventh Doctor's age was the same as the Rani's, namely 953. In Remembrance of the Daleks the Seventh Doctor said that he had "900 years’ experience" rewiring alien equipment. At the beginning of the 1996 television movie, the Seventh Doctor was seen to have a 900-year diary in his TARDIS.

The large gap in years between the Fourth and Sixth Doctors can be partially covered by the fact that the Fourth Doctor travelled alone for a time or with an equally long-lived Time Lady as a companion, allowing for several decades or centuries of untelevised stories to take place. Such gaps occur between the stories The Deadly Assassin and The Face of Evil when he travelled without a companion and between The Invasion of Time and The Ribos Operation when he was accompanied by K-9. Another potential gap occurs between The Horns of Nimon and The Leisure Hive when he travelled with Romana. The Face of Evil also revealed that the Fourth Doctor travelled on his own at a point prior to that serial (the chronology of this is not revealed in the story, but the novelisation places it within the events of Robot, right after his regeneration).

While the Fifth Doctor was never seen without a companion, there was a period (between Time-Flight and Arc of Infinity) where he was travelling with Nyssa of Traken, who, not being human, may not have aged normally. There was also a gap just after The Trial of a Time Lord which can account for the difference in ages between the Sixth Doctor in Revelation of the Daleks and the Seventh Doctor in Time and the Rani. Likewise, the gap between the Second and Fourth Doctors is occasionally explained as part of the "Season 6B" theory. One other possible gap occurs between Seasons 10 and 11, when the Third Doctor was between companions and could have spent time adventuring on his own before returning to Earth, and UNIT.

In the spin-off novels, the Seventh Doctor celebrated his 1000th birthday in Set Piece by Kate Orman, and the Eighth Doctor declared his age to be 1,012 in Vampire Science by Orman and Jonathan Blum. The Eighth Doctor also spent nearly a century on Earth during a story arc spread over several novels.

In the 2005 series, the Doctor's age is stated in publicity materials as 900 years, and in Aliens of London, he says, "Nine hundred years of time and space, and I've never been slapped by someone's mother." Rose follows up by asking him if he is 900 years old, and he replies affirmatively. He restates his age as 900 in The Doctor Dances.

How this figure is to be reconciled with the Doctor's age in the rest of the series and other (arguably non-canon) sources is uncertain. Possibilities include the Doctor estimating his age (900 years being "how old" he is, generally speaking, rather than his specific age) or lying about it out of vanity (in The Ribos Operation he gave his age at 756, although Romana insisted it was 759).

Another possibility is that the Doctor is simply referring to the years he has been travelling for simplicity's sake, as opposed to his physical age. In The Empty Child he speaks of 900 years of "phone box" travel, which, if he began at 236, would make him 1,136 years old. This figure does fit roughly with the Eighth Doctor's period as chronicled in the spin-off media (including his century-long exile on Earth). In fact, considering that the TARDIS did not acquire its police box shape until it landed in London prior to "An Unearthly Child", he may be even older. Of course, all this also presupposes that the figures given correspond to Earth years and not Gallifreyan.

The oldest The Doctor has claimed to be in the TV series is 953 when, in Mark of The Rani he uses that figure as a code to open a door, remarking that he and The Rani have the same birthday. But in the 2005 series he claims to be only nine hundred, although that statement was rather inconsistent anyway. He talks about being nine hundred years old but having travelled for nine hundred years, too. Assuming he hasn’t been travelling non-stop since he was an infant, that would make him much older. It is one of the problems with a long-running show about a single character written over the decades by dozens of different writers.

So, basically, I decided on a compromise. I made him 949 in my first story, which seems consistent with the length of time he has been adventuring in time and space, though slightly at odds with the 7^th Doctor’s age. He becomes 950 in this story, and into the bargain we scotch all those rumours about him being cloned, not born. As for his choice of where to celebrate his birthday, after the trauma of his encounter with the fantasy of his first wife in the previous story it almost stands to reason that he would want to be with family.

In the previous stories involving Susan’s children we learn that she has nine year old twin boys and a newborn baby girl. But none of them are named. We still don’t have a name for the girl in this story, but we DO learn that the boys are called Chris and Davie. And yes, it IS a total coincidence that this means they are named after the latest two actors to play the role of The Doctor. But their names fit within the storyline, too. Susan DID marry a Scotsman called David Campbell. That is a matter of record within the canon of Doctor Who. It made perfect sense that her eldest son – by a few minutes – would be named after his father. And having established in Pyramids of SangC’lune that The Doctor’s son, Susan’s father, was called Christopher, it stand to reason her other son would be named for him – if not for The Doctor himself. In any case, those names seemed to fit them like a glove and their separate personalities begin to slowly emerge, not so much in this story, but in those still to come. David’s issues with The Doctor are inevitable though. He is a little afraid of what his own sons are capable of, worried that their alien blood will set them apart from ordinary boys. He is also – perhaps understandably - jealous of the attraction of The Doctor’s world for them, travelling in the TARDIS with him, seeing wonders. A potential difficulty is hinted at here to be drawn upon later.