Actually... they kind of do. Calcium, phosphorus, iron, copper, manganese and zinc are all excreted in the fish feces. as well as some nutrients are released directly from the fish in the urine or gills to the water, such as boron, potassium, magnesium, molybdenum, sulfur and carbon.
However, I read an article that simply stated, pointed out that the fish food (depending upon the contents of the fish food) and other things in the water (mostly being produced through the fish) can be enough to sustain the plant. I pointed this out simply because the OP was worried about adding fertilizer and seemed to not really want to deal with it.
happy owner of a wild type GFP axolotl named Percival and too many guppies to count.