Get a receiver rack. I have even prefabbed a hunting blind and hauled it into the woods with one.
Yep, they can be had for as little as $50 or you can build your own if you or a buddy welds. Be sure to have some rope and/or ratchet straps to tie the critter down with.
Quarter, receiver rack, or the cheapest - large concrete mixing tub in the back (no rear seat). However, some guys have a fear of the creepy crawlies leaving deer and getting in vehicle. You could always bug bomb later.