That is a hilarious request! We see it every year, too.

The only grass that comes close is St Augustine and not Floratam. If that is all the damage your dog has done, then St Aug should work. It will need deep water once per week as will ANY grass you put in. The difference with St Aug is that it's the only southern grass which will tolerate any shade. And it will tolerate a lot more than you have. Chances are you already have St Aug back there. If that's the case you can nurse that until it spreads to cover the entire area. All it needs is weekly water and mowing at the highest setting. You can mow once per week or once every 2 or 3 weeks. If you want it to fill fast, then I would fertilize with an organic fertilizer once per month. I like alfalfa pellets at 20 pounds per 1,000 square feet as a fertilizer. Get it in 50-pound bags at your local feed store - sold as rabbit chow. Apply by hand for that small area.

Water deeply once per week. Deep means a full inch as measured by several cat food or tuna cans set out in the yard. For that area I would use an oscillator sprinkler. It might take many hours to fill the cans, so don't be surprised.

Don't look now but your dog photobombed your picture.

Thanks for the advice! :-)