I do like it and think you should go for it if it's a name you love. To my ear it's a very welcome change from all the Archies, Alfie's, Teddy's and Freddie's that seem so popular.
However, if part of the reason you like it is that you want an unusual name I would be prepared to find that it's more popular than you think. I do know a couple of Foxs between the ages of 4 and 1. Nature and animal names do seem to be having quite a moment so it may be a name that gives away their age as they get older.
I wouldn't be put off by people saying "what about when they're older" and such, as names have changed a lot and by the time they're old enough to have Fox Smith on their CV or be attending meetings with C.E.O's or whatever it probably won't be an unusual name anyway.