I love shopping for my bettas. I've read people using that heater in small bowls being pretty happy with them. i really like auto shut off function too.
I have to agree, the plant will grow to big for a 1-gallon space and I wouldn't like to use fertilisers in a tank that small, either..
+1 to the java fern - it grows whatever you do to it, pretty much. Java moss is another good plant, it's soft and billowy, doesn't need a lot of light and bettas love to rest in it - plus it helps keep the water nice between changes.