i got a kid carrier bike trailer for 25 dollars several years ago and it has worked great for packing out animals. I bolted some steel bar across the bottom to stiffen and strenghten the carrier. I have packed out whole deer on 3 occasions. This last year a friend who has a similar trailer and I each loaded half of my elk into our trailers and took it out in one trip down two miles of rough road. I figure we each had 150 lbs loaded. Since i was unavailable he packed his elk out by himself in two trips earlier that season. He has also used his to pack out 3 bear.
I take a pack frame in the trailer when I head out to hunt so that when i get an elk down I can pack the quarters to the trailer and then ride out. Like Tim has said a few times, make sure your brakes are in good shape. It is not easy to stop when 150 lbs of deer are pushing you downhill and your brakes are worn out.
I have also let a friend ride in the trailer when leaving an area for the day (he weighs about 160 lbs). Doesn't hurt to pack a pump and tire patch kit. If I'm feeling paranoid i lock the whole setup to a tree, but since I use the bike to get further in and away rom the crowds I don't normally see other hunters.
Get a good bike, get a trailer and go the worst case scenario is something breaks and you end up packing it on your back like you would have done anyways.