It is darn cute as a nickname,. but I agree with
Andromache and think it is far too infantile and fluffy to work as a full given name.
To be honest I think Pixie as a full name sounds woefully porn-star-esque.
I think Pixie could work well as a nn for
Patricia (Pasty reminds me of Pixie),
Beatrix, or even
Elspeth.