If your q is are you too old to have fun surfing then I'd say just asking that q proves that you are still pretty young!

If your q is really are you too old to really rip out there then I'd say it all depends on your ability to pick stuff up quickly and how athletic you are to begin with.
I started last year at the ripe old age of 39, am a chick with a typical chick's lack of upper body strength, and I am having a blast learning! Yup, I get tired but so did my 23 year-old niece who gave out before I did a couple of times out. If you are passionate about it, you can do anything! You're going to love it! Have fun!
Oh yeah btw, I really think all the people on here are telling you to get a bigger board because they know it will help you learn faster to do the basics and you won't get beaten up so badly. Maybe you could rent one just to see if it makes a difference if your short board seems to really be giving you headaches.