Goldfish have a tendency to grow like weeds and eat like pigs. My newest goldfish eats like 3-4 times a day. He becomes a shark when the food hits the water.
In terms of care, I agree with everyone that betta are much easier to keep than goldfish. My goldfish tank requires the most water changes, specialized food, and specialized plants. As an example, by volume I remove more water on a weekly basis from my goldfish tank than I do from my two 10 gallon (37 L) betta tanks.
A betta in a 20L (6 gal) tank would be a great fit. Perfect size :)
Quick question, is your goldfish a fancy goldfish (double tail, chubby body) or a common goldfish (single tail, slim body)? This impacts the final size tank you would need. Hopefully we can help you keep the final tank size down.