It is! I actually prefer just
Jenny (or
Jennie) and I like the fact that it was a medieval diminutive for
Jane, but I don't know if it's too nicknamey. I usually don't like nicknames used as first names. I guess if I used it in real life I'd just put
Jennifer on the birth certificate and call her
Jenny most of the time.
It's interesting that in the US
Jennifer is considered very dated to the 70's/80's, but in the
UK it was in the top 100 in the early 1930s. I know Jennifers in their sixties and seventies - including my cousin's grandma. :)