Trap shooting is good practice, but here in Oklahoma, we don't have very many flying deer. I would suggest finding a Bodark tree (or horse apple tree)
and gather up a bunch of them. Have a friend roll them on the ground, and shoot at them with a .22 rifle. This is the way we practice for rabbit hunting, and it does not cost you a fortune. The apple rolling on the ground forces you to pick your spot as it rolls between shrubs and weeds. This is more like the background you will be shooting at a deer. If you get where you can hit the apple on a regular basis, then you will be able to take a more confident shot at a moving deer. I don't like moving shots at deer, and I stand hunt exclusively anymore, and generally I don't have to take a moving shot, as I have the element of surprise, most of the time. If you are a stalk type hunter, I do see the reason for wanting to be good with a moving target though, and this is one of the best and cheapest ways to practice.