I don't mean to be contradictory, just offering my own experience here. I have that exact tank for my betta Guppy and I have a small Tom filter that I modified. I had it without a filter and must say life is much better with than without.
I baffled it with extra foam on the outside and in the outflow. The extra foam provided enough surface area that my tank cycled, all by itself. I also added live plants which also help a great deal with water quality. Now I only have to do water changes every other week instead of twice a week.