I've seen a lot of girls do some amazing covers of Beatles songs on acoustic guitars. There are some easy ones out there, even for beginners. Check YouTube by doing a search for "Beatles cover" and you'll find lots of girls doing these.
If you can do barre chords already, try learning "And I Love Her." You could change the lyrics to "And I Love Him."
It's a nice slow song with only a few chords and an easy enough picking part and solo, though it does lend best to at least a duet. You can figure our a single arrangement, I'm sure.
Many other songs in the Beatles category, but I'm biased; I'm a Beatlemaniac!