My 2.5 gallon doesn't have a filter either, just a bubbler to keep surface film at bay. I do 25% every 5 days and test for ammonia weekly.
If you want to, I think you can try is a big handful of hornwort and just 3-4 very large river rocks and setup your 1.5 gallon without the fish first. Get a desk lamp with fluorescent light, like 9watts and turn it on for 3-4 hrs a day. hornwort is tough and generally don't care much for light, 9 watt fluorescent is plenty.
I have a bucket of hornwort that hangs outside all day with no filter/anything and I dose 1ppm of ammonia, they use it up within 48hrs. Hornwort is very good at using ammonia compared to other plants IMO. They don't need to be planted either, just float them. They do grow very fast under good conditions, you can have too much very quickly. I have 1 strand that ended up close to a meter in length. I am sure someone out there has some for free. :)