Congratulations!
As long as you stay away from the obvious (and included in the films!) Arwen/Galadriel and Eowyn.. I think it is a nice idea.
If you want something that isn't obviously ME but you know it has an elvish meaning there are things like Linda (beautiful ) and Lorna (asleep!) or Laure (golden). Rianna is "crowned/wreathed" in Quenya and is very close to the welsh name Rhiannon.
Or you could try and translate something into elvish....
http://home.netcom.com/~heensle/lang/elvish/elvish.html
Or how about Melian? Tolkien name, not too obvious oroutlandish and a lovely meaning for a baby "Dear gift"?