The reason for 6 months as a minimum is just to have enough time together to get a pretty good idea that you are going to be together for a LONG time. Your kids don't need to "date" your dates - too much loss for them when those relationships break up. Sounds like you are feeling pretty positive about this relationship and I agree, 3 weeks probably doesn't make much difference in your situation.
What I WOULDN'T do is jump right in to being the Brady Bunch. Take it slow. You don't have to go from first kids' meeting to spending every weekend together with kids. Meeting the kids will give you the chance to see how each other are as parents and a heads up if her kid is a monster of some kind. But I would still keep kid interactions at a slow pace after this for a while.
Also, cool it on the PDA at first. I was 15 when my mother first started dating after my father's sudden death from a heart attack a year earlier. It was still VERY WEIRD to see my mom with another man.
