If you're thinking that this fish is suddenly a huge financial commitment, don't be too worried. You can easily find a 10 gallon tank on craigslist with filter, heater etc. for about $25. Plus, with a larger tank you can add a few more fish, which will really be fun for your son. Most fish have a hard time getting along with betta's but bottom dwellers do really well. You could try something like 3-4 corydora catfish, as they do best in groups and will add a lot more liveliness to the tank.
Just make sure you know about tank cycles before setting up this tank. It is very important that the biological cycle has happened in your tank so that your fish will not be harmed. If you google "fish tank cycle" you'll find many helpful articles on this.