I think it sounds fine, although I would give her a 'serious' name - as merrymonsters suggests, Emilia or Camilla, or Amelia or even Millicent (of Milly-Molly-mandy fame) - and use Millie/Milly as the nickname.
Thanks everyone I think you've helped me decide that if Millie's the name we really love we need to stick with it & forget the worries about what everyone else's opinions might be! Such a tough thing to pick a name that someone has to live with forever!
As title says i am having a bit of a wobble over the name we have chosen should we have a girl! Since about 12 wks we have been set on the name either Millie grace or Millie Sophia. The problem is baby's surname will be Morris & I'm suddenly panicking that Millie Morris sounds ridiculous! We're keeping our names a secret so can't run it past friends or family so just wondered what u ladies thought of Millie Morris?!