I think that different schools and different sororities do it differently.
If there is no ADPi chapter at your new school, you will go alum, even though you're still in college.
If there is a chapter, there, you may be automatically affiliated there, or you may have to go through a semester-long probationary period where both you and the chapter decide whether or not you fit in there. I don't think that they usually decide not to let you stay though -- it's mostly just a formality, and they wouldn't turn one of their sisters down.
You won't have to re-rush.