I seem to remember I purchased a PSE from Bass Pro when my son was that age. I remember i was going to give it to an old coworker for his son but he wasn't interested. I ended up giving it away to my god son a few years later after I upgraded the rest. It was pretty good with the new rest.
Kids do grow quickly. You may want to check out a woman's bow since they tend to be lower draw weight and do get into legal hunting weights. When it came to shotguns. When my son was 8, I went ahead an bought him an adult pump because I knew he would be able to figure out how to handle it and of course grow right into it. The gun was almost as tall as him and it was funny at the five stand. They both were the same price. So with a bow, the more your son draws and shoots, the better and faster he will develop the muscles required to shoot and may advance pretty quickly in DW. Good luck!