my 4 year old little now tells me, "Daddy, when I get bigger I can go shoot a deer with you too. Right?"
I look forward to the day she actually is big enough, I am just not in any big hurry for to get there though.
She is big enough now, just make sure you take a little time pre hunt to get her accustomed to slipping on some ear muff for the shot, should you take one. My daughter and all of my grandkids have been hitting the woods with myself and my daughter since they were able to walk good. While we don't shoot something every time out, they learn early what to do, when to be quite, and to look for movement. They will really surprise you.
Just make sure YOUR up to it. Hunting with them is a short trip usually unless the weather is pretty, or your in a box blind, or similar where they can take a nap. Haul an old blanket out some coloring books and such and go for it. When you get out there, show her tracks, and other sign of all the animals you can find, they soak it up like milk in cornbread. I started off getting them used to putting on their ear muffs when they heard me clear my throat. We could do it sitting in the house, the car, or where ever. Once they had it in their heads that meant get them on, then I had to get them to NOT say "where is he" or "are you going to shoot something", or simply nothing at all. The latter is the hard part since they do not realize they actually are talking louder. Sometimes it is a circus, and you end up blowing everything, but other times when it comes together they sit there waiting, eye's glued on the deer big as pie plates. It makes it all worth while, even if you don't shoot anything. One of the two best times I had, the first I had my oldest out when he was about 3 maybe, we set up a lawn chair and I had him sitting on my lap. Nothing else around us. I hit a grunt call a few times just to get him fired up, and low and behold, in walks a nice young buck. He came up to within about 15yds of us just sitting there, before he meandered off into the woods. Another trip with the middle and youngest, we were simply sitting on a blanket at the bottom of the hill on our farm looking out across the back pasture. Out of the woods 50yds from us comes a VERY nice 8 point, and he also walked up to within about 30yds of us and stood there looking like the king of the woods. Then he simply turned and walked off. I have no idea why he never spooked, the two little ones, ear muffs on, were popping up and down like they were on pogo sticks, and talking up a storm. All the while I am going SSSHHHH SSSHHH your gonna scare him off...
But like I said these are not hunts in the real sense of the word. These are time spent with your kid(s) that you and they will remember. They aren't long or drawn out ordeals and can be over before they get started good, or can last the duration of your planned time out. Trust me when I say, it might seem like wasted time on your part as it might pertain to actual hunting, but in a couple more years it will pay huge dividends in your relationships.
. 
