I kept unfiltered 1 gallon tanks for a while. A 100% water change should be done roughly every 5-7 days, which some people are unaware of. Partial water changes will not get rid of all of the crud an ammonia which can accumulate over time. And in an unfiltered tank, despite the popular belief, there is no community of bacteria that will help deal with that issue.
Filtered tanks are "cycled", which means that the bacteria has been established so that it can convert ammonia to nitrite to nitrate (nitrate is the least harmful of the 3). You can cycle with fish or without. Without is more humane, because your ammonia and nitrite levels will spike during the process, which damages your fish. I have done a few fishless cycles. They take roughly a month. First, you add pure, unscented ammonia to the tank until it hits about 5 ppm (even 0.1ppm is harmful to fish). Over time, you will see the ammonia levels drop as those bacteria are being established, so you keep adding ammonia so that keep it around 5ppm. As your ammonia starts to drop, you will notice the nitrite levels start to rise (nitrite is also harmful at 0.1ppm). Nitrite levels will reach a peak. The bacteria responsible for converting nitrite to nitrate will start to become established. Nitrite levels will fall and you will see nitrate levels begin to rise (nitrate levels are fine for fish up until about 20 ppm). When your nitrate levels rise, you do a water change and it is safe to add fish. When you do regular water changes in a filtered tank, you are keeping the nitrate levels low. When you neglect water changes in a filtered tank, you will see ammonia levels and nitrite levels rise as well as the nitrate.
Ahem.
Small bowls can go to crap quickly. I had a 2.25 gallon tank which I did 100% water changes on every 7-10 days. The only time I let it get to day 12 was the time my fish got popeye.
The ideal situation for someone who does not want to do massive water changes very often is to filter a 5 gallon tank. I kept a betta in a cycled 5 gallon tank and I was doing 10% water changes weekly, which is a lot less messy than 100% water changes weekly. With 100% water changes, you have to make sure the water you add is roughly the same temperature and you have to float the fish before adding him back so he does not get stressed out.
If you do not have a heater, I suggest you get one. You may be able to find ones suitable for small bowls, but I have used heaters ment for 5 gallons in a 1 gallon with no problem. Keeping the temperature between 78 and 80 is less stressful on the fish and will make him less susceptible to illness. Also, adding a teaspoon or less of aquarium salt (do not use salt with iodine) helps with healing and prevention of illness.
Also, when it doubt, get an ammonia test kit. At any sign of ammonia, you know you are over-do for a change. It may help you establish whether weekly water changes are appropriate or if you have to change it more or less frequently.
Speaking of goldfish, I always thought they were pretty cool. But since the rule of thumb is 15 gallons for the first fish and 10 gallons for each additional fish, I never had the room or the budget to keep them.
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Will keep good thoughts for an uncomplicated procedure and a speedy/full recovery for your furry friend.
But, then people will call me lame, shy, anti-social...not like I haven't gotten those insults before
