It is NEVER too late to start barrel racing. At 19? You have LOTS of time. I know several NFR Qualifers who got a "Late start" on the other girls.
I barrel race because its what my horses love and I have a "need for speed" that my trainer tapped into when I was young. I liked this event because it didn't require me to dress up, and I could put any color I wanted on my horse and just go have fun. For a little girl, that was the best thing ever. Sure I showed in other things as I got older (English, Reining/Reined Cowhorse, even some pleasure) but nothing ever stuck as much as barrels did. I loved training barrel horses and I loved riding barrel horses. This eventually evolved into me running in an association and then hauling to rodeos.
If you want to try it, then try it! It can't hurt. I know a lot of girls who ride English but come down to the association and run my horses for me just because its a fun thing to do to get away from the high level show world. (And I like it 'cause I get my colts seasoned low-level for free
) You don't have to be competitive right away, you can decide after you've ran a couple times. If you really love it, you'll advance your way through.