I agree with using Camille instead, that's a nice name.
Camilla = Parker Bowles, and if you're English she'll be Queen (or consort,whatever it is...not British so not particularly into the terminology). The association will continue to be very strong.
I think Millie is weak and wishy washy. You could also use Camellia. Personally I think it's too much name but you might like it.