Hi R. - as a child of divorce and dating, don't meet the kids until you have been dating for at least 6 months-1 year. No matter how much you both think that this is "the one", in the early stages of a relationship, you just can't guarantee it.
I don't know what kind of person your girlfriend is, but the fact that you're asking about this shows that you're a caring person. You may need to take the lead here and slow things down where the kids are concerned. My mom was more concerned about finding someone to take care of her (and supposedly us) that she went through a bunch of boyfriends during my growing up years. Some were nice, some acted like they couldn't be bothered. Some had kids, some didn't. Imagine what it would be like if people kept cycling into your life, you let down your guard for them because of the type of relationship it was "supposed to be" for your parent, then it didn't work out. It sucks.
So, go on dates with her - get past the glowy new relationship phase; but you need to think LONG AND HARD about this. You are not dating a single woman and having fun - there's nothing wrong with that in a no-kids situation. BUT - you are dating a woman with children (there are 4 people involved in this relationship) with the goal of getting married. If you're not interested in potentially being a parent to a 6 & 9 year old, then get out now. Otherwise, it's not fair.
Sorry to be blunt, but if more people who dated where kids were involved thought this way BEFORE the relationship got serious, a lot of pain could be avoided for everyone.