Gertrude's tail, kind of like Yertle's moon, is a stand-in for all of that stuff, stuff, STUFF in life she can't have and can't control. It's stubby, it's droopy, it's frizzy, it's only one color, and, simply put, it just ain't anything special. In that way, it's also kind of a symbol for all that Gertrude is: someone average, which is a-okay by us.
Sure, Gertrude can try to change it, but not without disastrous results. It's a good symbol for us to understand, living as we do in a society where everything is wrong with us and everything can be changed… for a price.