(Warning: This song gets annoying fast!)
The animal singing this song is actually some species of tiger salamander from north of the Rio Grande. An axolotl is a species of tiger salamander from the lakes that once made up Mexico City. It is a neotenous species that reaches full maturity while still having gills, which salamanders generally only have when they are larvae. Northern species of tiger salamander can be neotenous, but generally, this is a trait of the axolotl.
Salamander species that retain their gills into adulthood are called perennibranchiate salamanders. The name means “always having branches,” which makes sense if you have ever seen an axolotl’s gills.
Now, it is possible to get an axolotl to metamorphose. However, I don’t know why anyone would want to do it.
It takes a certain amount of know-how in chemistry to get the iodine levels just right to make the axolotl metamorphose. It has to be high enough to get them to metamorphose and low enough to keep from killing the axolotl. And if the axolotl has reached sexual maturity with its gills, the chances are that it won’t live very long as a metamorphosed adult.
Here’s a really good page on the metamorphosed axolotl and includes comparisons between those animals and tiger salamanders. Many bait shops carry larval tiger salamanders, usually under the (incorrect) name of “water dog.”
(A water dog or mudpuppy is another perennibranchiate salamander. It is not the same thing as the neotenic tiger salamander or the axolotl. Please do not claim that you caught an axolotl in Ohio or New York.)
If I had an axolotl, I would keep him in the neotenic state, simply because that is the life it evolved to live. It is the life neotenic and the life aquatic.
Finally, I should note that wild axolotls are quite endangered. The introduction of tilapia and carp to the lakes in which they are native has been very bad for the species. The fish eat the axololts’ gills and their larvae. It doesn’t help that these salamanders are found only in the lake system that is part of the largest city on the continent.