"We also have a creek that runs next to camp. Would it be smart, if I shoot one to, stick the meat in the creek while we back it out? Or would you hang it up?"
Get the hide off ASAP and then hang the meat in breathable game bags in the shade near the creek where it should be cooler than other areas. We do that and then put the game bag in a garbage bag inside our packs just long enough to keep our packs clean on the way out to the truck. That way the meat is cooling the entire time in the shade and is left in the shade in the game bags at the truck. Generally the meat is fairly cool by the time we get back to camp and it's never put in a cooler until it has cooled off even if we have to cut it into smaller pieces to speed cooling. NEVER put warm meat right into plastic bags, as they hold the heat and it's an easy way to ruin it.