Lowry,a lot of folks use a 5 gallon cooler for their standard 5 gallon batches, so I guess theoretically you could do 1 gal batches in a 1 gallon cooler or your kettle, even a small dutch oven type pot on the stove.
But I probably won't be the only one to suggest just building a 5 gallon mash tun to start. The cost of materials and time to put together a DIY cooler mash tun will be the same and you'll be able to use it when you step up to full 5 gallon batches. In that vein, I'd also recommend stepping up the recipes a little larger than 1 gallon. You'll expend the same amount of time brewing 1 gallon as you would 3, 4, 5 gallons, but you'll lose alot of volume to hops, transferring, bottling etc. Plus, you'll need some pretty precise measuring equipment with grain/hop quantities that small. My 2 cents