Agree with others -- cheapo inflatable raft of some sort will do just fine to tow it out, depending on the water, of course (river vs lake). Unless you actually kill something, you won't even have to take it out of the box. Just tie a rope around the carcass somewhere that's attached to your kayak so if the raft sinks, you don't lose your deer.
I've towed helpless canoe riders with another canoe in 20 mph headwinds. It's work but not impossible. As long as you have some buoyancy under the carcass (like a raft), then it should tow just fine for a mile or two. Much more than that will just require some longer breaks.
And if you can walk in, you can also walk out. Put the deer in the kayak & walk the shoreline. Or make 2 trips: first with the deer on foot & the a second with the kayak. Getting a deer is always a good excuse to show up late.