It's perfectly acceptable as a girl's name. There's a beautiful older children's book called 'Love Aubrey' which is about a girl.
I really like it and much prefer it for a girl than for a boy.
There were only 11 female Aubreys born in the UK in 2011 but then there were only 21 male Aubreys so not that different.
In the US Aubrey ranked at number 20 for girls last year but hasn't made it into the top 1000 for boys since 2002 when it ranked at 938.
So I think it's transitioning into far more of a female name really.