I am assuming you are not living in the UK so school is not so odd as it sounds here.
Firstly, congratulations! A first baby is exciting, scary and a profound experience. I hope you have a very ordinary pregnancy and a straightforward birth. Good luck!
I think I'd definitely wait till you are past the 12 weeks mark before you tell them, and yes, I was married young and had my first at 21. It was very hard telling my parents as like you we had only recently graduated and knew they saw us still as children.
We knew they would be excited about it BUT we felt they would also judge us for being somewhat reckless in taking this step before we were secure financially.
What I would say now is that yes, you are young and don't know where life will lead you, but being young you are adaptable, have plenty of energy and (I hope) love each other and will do whatever it takes to make this work and to give the little one a good life.
Tell your parents, if you found them to be kind and loving, that you have learned from them and know you can do it. If you tell them that you are confident they will worry less and you will slowly begin to believe in yourself too.
Keep saying to yourself that you can do this and have great things to look forward to.
Our reactions as new grandparents are going to vary according to our own lives, our hopes and dreams for our children and their partners. Please believe me though, it would be an unusual grandparent to not have at least a little joy for you! I suspect you feel you are dashing their hopes for you to have an "exciting career".
You can still have a good career but are choosing to do this now.
This post is a bit garbled I'm afraid. It brings back the anxiety around telling my parents (who loved me beyond measure). I do understand where you are coming from.
They will continue to be proud of you, and will surely love your little one too when the time comes.
Good luck.