I'm not sure about Michigan laws, but in New York, you must be age 12 to hunt small game, and age 14 for large game. Both require an adult to accompany them. Therefore, you might be spinning your wheels a bit early. Give the little one a cam-corder for now, but by all means, if she's interested, take her to a good archery shop, and have a look. There are many bows out there that are appropriate for her, and they get traded in for new ones as they get outgrown. I'm sure that you can find a relatively inexpensive used bow that will fit her for a few years. Then, all you have to do is SHOOT it ! A static target in the basement or the back yard and a dozen arrows will provide hours of fun and build shooting skills that will last a lifetime. If you don't shoot a bow, you might give it a try. It's alot of fun. There are always archery leagues, 3-D shoots, and indoor ranges at many (if not most) good archery shops to give you an oppertunity to have fun. I shoot my bow year-round. Yes, I bought it primarily for hunting, but the truth is that I spend WAY more time at leagues and 3-D events than I do in the woods.
Find yourself a few good archery shops, and talk with the pro about your situation. They will all have suggestions and give you advice. Don't buy the first thing you see. Look around for a while and find the bow that will grow with her for a few years. My suggestion is that you NOT buy a "Genesis" bow. They are made well, and have a couple great features, but they will not serve you well. Here's why: The Genesis bow has no fixed draw length. That is a great feature if many different people will be shooting it, but if only one person is to be using it, you will find it much easier to be consistant with a bow that draws the same every time. Also, the Genesis bows have no let-off. Again, having proper let-off will allow for better archery form, and therefore better accuracy. The Genesis bows are SO underpowered that they will not propel an arrow more than a few yards with enough force to stick the arrow in the target. The Genesis bows are really only good for learning the first few basics of shooting a bow. She will outgrow a Genesis bow in a week, maybe sooner. You would be better getting her a fiberglass recurve bow than a Genesis bow. As for arrows, don't mess around with cedar or aluminum. Carbon arrows are expensive, but they last a long time. They never bend, and they are tough. I like GOLD TIP arrows, myself.
You must understand that archery is all about form. Proper form will lead to incredible accuracy, and the lack of good form will undoubtedly lead to poor accuracy. When you find the right bow, make sure that she gets good instruction to go with it.
Also, don't buy into all the hype of the latest and greatest. By that, I mean, get a very basic arrow rest, like the WHISKER BISCUIT and a very simple sight with no more than three pins. A release is going to be necessary, and there are hundreds of them on the market. Let your archery shop help you with that, but make sure that the one you buy has a wrist strap of some king, and has a trigger that is not likely to be tripped accidentally by a new shooter. Bows are not toys. They are indeed dangerous if used improperly. By the same token, they can be a source of great fun, challenge, and bonding with your little girl.
Have fun, and be safe.