One or two months?
In that case you'd definitely want to dose ammonia, yeah. You don't have to do much though. Nitrifiers can go for months ammonia-starved before really showing declines in nitrification capacity and/or populations. So this is more just out of an abundance of caution than anything - just dose some ammonia every two weeks or so. 2ppm should suffice. If you want to be even more careful, you can dose 2ppm weekly.
As for moving - usually if you can keep your biomedia submerged in water, that'd be best. Failing that, wrapping them up in damp towels or paper works. If the move is not too far, it's not as much of a worry. How far are you moving? Or rather, how long do you reckon the biomedia would be out of the water?