oh I see! well you have to time travel and wait until Nibbles pings you telling you that she wants to move. When she ask, you just have to say yes that she may move out. If you dont have high level friendship with her (not do favors, write letters etc) then she can change her mind even you told her to move. If she is fine with leaving, she will give you a date in which she will move out, you time travel to the date she is moving out (not after) and when she is in boxes, I come to your town and ask her to move to my town.
you can try to move her out but this is your first time so it might take awhile. I dont know when your last villager ping for move out was. If you do know, the next ping will come within 3days-7 days.