Your son is only 19, so there is still a probability that he will have a different girlfriend by the time he's 25.
I think the girl made the right decision in not meeting the folks until she was sure she liked your son enough.
I remember in my youth going out with a handsome guy only four times when he said my mother wishes to meet you
He introduced me to his mother and left me there to be interviewed by her whilst he left for 10 or 15 minutes, she asked me if I really liked her son? that he was going to be a doctor one day, what job did I have? what were my hobbies? then she tried to make small talk about my family background.
I had another 2 dates with him whilst planning how I could run.
To me he was just a good looking date, marriage with him was far from my thoughts and meeting the family was the last thing I wanted to do, no matter how he might have felt about me.
Good idea on inviting your sons girlfriend to dinner, I wonder if her family have met your son yet?
Let us know how it all goes.