I have 3 daughters. The oldest likes to go, the other two are sissies. I take my 5 year old everywhere. You won't kill near as many critters, or catch as many fish, but it really doesn't matter. Buy twice as much food and 3x as many crickets as you think you need. Be prepared to go home as soon as you get to your hunting/fishing spot. Don't take them when it's too hot/cold. I let mine pick out all her own hunting clothes to make her feel special. It makes her want to go just because she can wear those clothes.
Teach her to sneak up on squirrels and such, and the next thing you know she'll be trying to sneak up on your neighbor's peacock "just to pull a couple feathers."