Ok, here is more info.
The song was published originally about 1880 in Scotland, and was popular in America. J.J. Sullivan was probably not the original songwriter, and James Rolmaz rewrote the song again with added lyrics about the Prince of Wales for music hall performances in 1901.

I am sure the song was popular in Tombstone, Arizona by 1881, because it was involved in a shooting late in the year.

The short version--A man who had been drinking bought a new shirt, which was loud in color, with garish stripes. He put it on in the store, and everyone on the street began teasing him as in the song, with "Where Did You Get That Shirt?"

At first he thought i was funny, but as it went on, he became angry, and was heard to mutter, "the next sonofabith who says that is going to get shot." And, as luck would have it, his best friend, equally tipsy, walked up to him, and asked the fatal question. The man drew his gun, and fired twice at his friend, who fired back, but at the third shot was struck in the mouth and was killed.
Reported in the Tombstone Epitaph

Great history on this little ditty!