I would take her to your parents during the actual move because you and your hubby are going to be busy with moving everything, plus doors will probably be left open for the movers to get stuff in and out easier, and you don't want her to run loose or get stepped on, or something dropped on her.
Also, to make the move less stressful I would (if your able too) take her to your new home with you a few times before you move so she can check the place out. When we moved into our house we did that, (even though it wasn't exactly finished) and the day we moved in I brought him and let him check the whole place out. He adjusted pretty well, but then again he thinks every place is "his place"
Good luck with the move!