Yup, half an hour is great! I just wanted to make sure you were adding water rather than just letting him acclimate to the temp by floating him in the tank.
Where is Winnipeg?
Anywho, yes Nitrogen Cycle is very important but since it's a 1 gallon and assuming without a filter, it won't matter to much for that. But basically there are good Bacteria (Beneficial Bacteria or BB) that keep your fish safe from bad levels of ammonia (fish poop, left over food and more), nitrite and Nitrate. Ammonia, Nitrite and Nitrate are the bad guy's that are always there and the BB are the good guy's coming to eat up the bad guys and save your fishy ^_^
But the Cycle won't be stable in tanks under 3 gallon's really so you won't really have to worry about it, instead you'll have to do twice weekly water changes to keep the tank healthy. Or for now you're doing daily? water changes to keep him healthy? What else is wrong with him? If he's just stressed then you don't need to do daily water changes.