I think you are an excellent father for not depriving your kid any fun simply because she is a girl.
As long as you are teaching the safety aspects you can't go wrong.
When I was a kid I joined this scout like organization where they asked the parents to give you a knife, so I got one when i was 7. They taught us how to use it and how to be safe. Because it was done at an early age, we didn't forget what we learned and we all show the same respect for knives as adults. I'm clumsy and accident prone, but even I never had a outdoors knife accident. Ever. (Now they should teach kitchen knives safety too...)