The name sounds really manly. I wouldn't use it for a girl. I'd go for
August,
Augustina or
Augustine. (Although
August doesn't sound feminine at all, I still prefer its cadence over
Augusta). And I don't like it enough to use it for a boy.
As for naming your child after their birth month..its kind of corny, yet reasonable. I don't think its "tacky".
Name These Characters 1 (over)
https://www.behindthename.com/bb/game/5316320
Name These Characters 2 (over)
https://www.behindthename.com/bb/game/5327763
Name These Characters 3 (over)
https://www.behindthename.com/bb/all/5332744