My mom got a new house when my son was one year old. The first time we went to visit, she had purchased a few toys and a child-size bean bag. She kindly made it clear that these were not "gifts" we were expected to take with us, but rather the beginnings of her "Grandmother toys." She wants to have a corner/chest of toys when any child comes to visit. I think the important distinction is that my son plays with them when we visit, but they are not our responsibility. I would recommend sorting out your daughter's favorite toys and definitely taking those with you. Try to remain realistic about many factors: 1. Weight allowance for the move. 2. Space in your new quarters. 3. Age appropriateness of the toys. 4. Gift-giving holidays approaching. When I was a kid, I used to go through a toy purge every fall to prepare room for my Christmas loot. Now that I am a mom, I often find that sorting my son's toys is much harder. I remember who gave him what and when or times he played with it.... but I appease myself with the fact that I take lots of pictures and the memories are not in the things. (Thank you Clean House and Clean Sweep.)
After your sort, allow your parents to "shop" through the remains. Let them pick out what toys they may want to keep around for your daughter (or other children). You may (or may not) want to offer that option to the other set of grandparents (if they're in the picture) or anyone else you may visit frequently. Then the rest can be donated or discarded. I think that system holds benefit to many. Good luck!