1: The New Planet need not be close, for travel to be easy. If depends how you want to travel - cheap or often.
2: The problem I imagine is the atmosphere. There's a LOT of it needed to make a planet habitable, more than I suspect we are likely to find in the asteroid belt. The asteroid belt is theorized to be the remains of a planet or moon, and most of the atmosphere was lost, it does not remain there , if I remember my astrophysics correctly.
3: The other problem I imagine is the self-replicating robots themselves. Such Von Neuman - machines are an interesting concept, especially considering nano-technology, but wether it is workable.. well, it's a challenge, but we're talking the future, and it would be folly to say it will not be possible.
However, unlimited industrial capacity does not mean unlimited power, and such a robot horde would nearly need both.
I would ocnsider a space lens, to gather sunlight for heating the planet, rather than nudging it to a near - earth orbit. This could also, during construction, be used both for heating the planet core and an energy source.
Another problem, which I take less seriously, is that usually mentioned in science fiction - for some reason, such machines are almost invariably described as extremely dangerous and destroying their creators - the Berserks, for instance, or the machines in the terminator movies - or for that matter, the Matrix.