Everyone PT has got to start somewhere. I would ask to see if they have any references. I would also find out more about their fitness background, experience, etc. By the time I was 19 I had been training for 4 years, reading up on the science behind strength training and conditioning, and implementing those things on my own personal program development.
Do I know more now than I did back then? Of course I do, but that's because I've continued to educate myself, staying up to date on all the current research as it pertains to the human body and how best to train it.
However, would I have been able to put together a safe and effective program for a person trying to lose weight and improve their general fitness? I definitely would have.
I think David the PT and I are both trying to say that age isn't the biggest factor, experience and knowledge is.