Just a little food for thought…
At the beginning of “Rise of the Cybermen,” the TARDIS crashes in Pete’s World. Why? The Doctor says, “The time vortex is gone. That’s impossible. It’s just gone. Brace yourself! We’re going to crash!” So, Pete’s World doesn’t have a time vortex. The TARDIS travels through time and space by going through the time vortex, so if there isn’t one, it can’t travel in time. It can travel in space because it can fly normally (and it’s pretty darn fast, since, in “Journey’s End,” it tows the Earth from the Medusa Cascade back to the solar system in less than a minute) and it can dematerialize to hop between universes, but time travel in Pete’s World, at least by TARDIS or vortex manipulator, is impossible. (Ha, maybe zygma energy might work in that universe.)
The other question is, are there Time Lords (other than the Metacrisis Doctor) in Pete’s World? Probably not. Before the Time Lords created the time vortex, they were simply Gallifreyans. Either the Gallifreyans never created the time vortex, in which case they don’t have the power they have in the Doctor’s universe and are not “lords” of time, or the time vortex was created but destroyed, so any existent Time Lords no longer have their primary tool to watch over and manipulate time.
Ok. That thought’s been bugging me ever since the David Tennant celebration in the theater. I’m done now. That is all.