Dunno about that, sets are supposed to be dismantle-able... they did it with the previous one at least once. I'm surprised they managed to keep this a secret, a console room change is almost like a new companion, really!
Unfortunately, the season 5-7 console room set wasn't made to be dismantled. They had welded it into the soundstage beams, probably for stability reasons. Oddly, I think it would have been easier to move the 9/10 console room (assuming they didn't finally strike it after "The Doctor's Wife").
One interesting possibility next year is that there could be a Hartnell console room standing set, thanks to the Gatiss drama about the creation of Doctor Who
. Its construction would come out of that film's development, but it would be available for Doctor Who