Between the time he leaves in the TARDIS and then comes basically right back to tell Rose it is also a time machine.
The idea that the Doctor does all of those things that Rose saw the documentation on (like the
Titanic) in that brief moment at the end of "Rose" doesn't sit right with me. It's too, and I hate using this phrase,
timey-wimey. If the ninth Doctor were a Moffat creation, the Doctor doing stuff
after Rose is aware of the Doctor doing stuff wouldn't bother me as much; Moffat's Doctor is an ontological mess that should collapse under the weight of his own recursion. But I can't think of any time that RTD played the timey-wimey card in that way; RTD's Doctors traveled through time, but they did so in a linear fashion. Yes, it's
possible for the Doctor to do something like pop off for a few years and come back to where he started, but there's nothing in RTD's text or his portrayal of the Doctor to support that kind of reading.