Only you are the best judge of your relationship, but after a year it does sound pretty solid and it's kudos to your g/f for wanting to meet them and be a little part of their lives. I wouldn't bow to pressure from your g/f if it doesn't feel right, but I think also that to see it from her point of view is useful also.

You can't protect your children from everything all of the time, and the future is always unknown, but we shouldn't let 'what if's' rule our lives. Caution is good but it's not like you've been introducing lots of various 'special friends' along the way.

Good luck with whatever you decide to do.