A workable idea, but we should avoid directly imitating another work. Draw ideas from it and develop them surely, but not ape them directly.
If you've already strayed from Battlestar Galactica's drives in your synopsis, then I apologise, I'm not familiar with the show.
While jumping around within combat would be difficult, I would imagine that one might be able to make a jump out of combat with little worries. Leaping, say, an AU straight up from the orbital plane of a system would put some distance between you and an attacker, and the space up there is pretty empty so a precise jump wouldn't be needed.
No unified government, possibly, but minor planet? Much of H2.0 would still be terran, and Earth supported a corporation which grew large enough to split off and form it's own faction.
Sci-fi focusses on Earth for a reason. The readers are human. The characters are frequently human, so that we might associate with them. And humanity, as a whole, is rather attached to the insignificant little blue planet. We happen to live here, after all.