I love
Elizabeth as well, especially the spelling
Elisabeth. I would use the nickname
Ellie. I know several women with the first name
Elizabeth, and even more with the middle name
Elizabeth. Many go by
Liz or
Beth. My sister is
Elizabeth, but goes by her middle name. Most of the Elizabeths I know are between 18 and 25, but I know older ones too.
I believe all of them go by nicknames, but I don't think it's too unwieldy to use without a nickname. It seems to me though, that if you dislike a particular nickname, you should at least use a short form you like from time to time. Then at least she'll have a starting point once she gets to school.