This is MumsNet Coco777 so basically, you should NEVER meet his children. Certainly not until they are at University and even then should avoid being near him when they are home. !
Back in the real world I would say that 6 months is long enough to be together before meeting them. However I do just mean meeting them as 'dads friend' . No sleepovers . Just days out, maybe stay for supper etc. My reasoning is that the relationship you two have now without dc involved is not remotely like 'real' life with kids. At the moment you can focus on each other but the moment kids are involved the dynamic changes. It makes it a different relationship.
A lovey-dovey relationship with him being the ideal boyfriend may suddenly make the stars fall from your eyes when he does some of the really common bollocks that non-resident dads try to get away with.
For example,
Truly shit parent who just doesn't parent. Nightmare out of control kids.
Disney dad that says yes all the time even to poor behaviour because he feels guilty about the split.
Upset kids who need him to help them negotiate your new relationship with him (and therefore the reality of never getting back with mum)
Sad kids, whose father doesn't try to talk to them about their feelings.
Really common.
The lazy arse dad looking for someone other than him to to do cooking, cleaning, childcare when they are with him.. leaving it ALL to you.
Over the next 6 months of casual meetings you will REALLY know what sort of man he is WITH THEM. Then you can move forward to a more permanent role or slide out of the relationship with much less impact on the children's lives. Bollocks to waiting another year or two before you find out that it's not for you !
However BEFORE you are even mentioned in earshot of the DCs , one really important piece of advice. Get your DP to download the papers from HMCTS for a Child Arrangement Order and get it into the court. It cost £215 and the norm these days is to do it without a lawyer. Get him to get his child contact regularised. The minimum should be every other weekend overnight Friday - Sunday evening with an evening every week after school. Because as sure as eggs are eggs, the moment a 'difficult ex' has scent of another woman on the scene, she will withdraw/be difficult with contact. Do this now and if all goes well, he will be having regular contact that is set in stone before you become an official 'partner' in the eyes of the kids and this type of abuse of child contact can be scuppered.