Of course it would be a great idea! These days there isn't so much etiquette when it comes to showers and such.
I had shower and I was not married when I was pregnant with my son...15 years ago. She deserves a shower like everyone else!

Also, I must say...looking at your pic on your little avatar...You do not look anywhere near old enough to have a 19 yr old....I thought you were in your early 20's. You go girl!