First of all. no question is stupid! Second of all, I agree with Luke but if it was me I would get a filter, but an inexpensive one, battery operated maybe? Best of luck to you!
A betta can be housed in a 2 gallon fine without need of a filter.. You could also keep some shrimps as well if you had a few plants in there... You wouldnt need to change the water but once a week.