@puzzle76,
Firstly, I'd consider things deeper and more carefully. Her relationship with her parents is being jeopardized because she chooses to lie to them about this. It's certainly not a mature response. That behavior never bodes well for a future for the two of you. Her (and your) integrity is/are important.
You have to seriously consider her future and her future relationship with them. A young woman needs to maintain a close relatinship with her parents. I'm hoping you realize all of this. Don't get caught up with the passion of the moment.
As an aside, a woman at the age of 20, no matter how mature, still is at a different stage in life than you are at 34. I assume she still lives at home with her parents? This may balance out in a few years as she gets more established in life and her career. Until someone is out on the own and paying rent, etc., you are at different stages in your growth.
Secondly, both of your work relationships is/are also affected should anyone find out (particularly your bosses and/or her fellow employees).
Is it possible that one of you can change jobs..transfer to a different department? Boss/worker relationship can often be loaded time bombs that can get people fired or cause career setbacks.
A cooling-off period might be a wiser idea. You can always revisit things in time if there is still the desire, but as long as you are boss/worker it's really not wise.