You want to get some Pimafix (Or Jungle fungus rot as you did, it all does the same job) , Melafix and aquarium salts in that tank, daily water change with dechlorinated water ... a 1 gal is a good med tank, and I have dealt with some pretty sever fin and tail rot. If you don't have Melafix then Bettafix will do just the same.
I currently have a very little girl in a 3 gal and do a full tank change daily, it's just an under gravel filter but for a day it is good, her water comes from a filtered tank daily, my last case of tail and fin rot recovered pretty well and I seen good growth before moving him to a 10 gallon tank, he still gets the Pimafix just in case since he is recovering from a very bad case of rot and his tank gets a 1/3 tank change every 3rd day.
Keep us informed on how your little one is doing.