She doesn't need the band for anything at that age. My 1.5 year old son won't wear his. I just threw it in the bag and haven't looked at it since.
If you go after she turns 3 and she still doesn't want to wear it, you can get a keychain ($10 at many stores at Disney) and put the Mickey head in there. This is what I did as my band kept popping off (I actually lost it twice).