Going against the grain slightly here but I am personally of the opinion that children should be introduced sooner rather than later. Not to a string of flings, but the reality is that children do change the dynamic of a relationship, and there is little point investing a year or more in a relationship if the DC are going to change everything at the point of introduction.
You can introduce someone as a friend without needing to talk about the potential seriousness of things at first, and just see how they get on and then take it from there.
With regards to moving in, I would leave it at least a couple of years until you’re out of the honeymoon period. Because many children who do take to a new partner straight away will become more trying as things progress, not least because kids change as they grow up etc, and it’s a lot harder parenting someone else’s children and maintaining that level of tolerance if the kids aren’t yours, iyswim.
My dc was nine when he met my partner, but it wasn’t through my decision. They got on and still do get on nearly six years later, however although we wanted to move in together quickly at first, circumstances meant that didn’t happen, and now six years down the line I have a sometimes stroppy teenager and a partner who do get on, but it’s beneficial sometimes to have the time when DP goes back home (and we are long distance) if he and DC have e.g. clashed a bit over the weekend, and then it is just me and DC which often works well iyswim. As things stand we likely won’t move in together now until DC leaves school, and in retrospect that is not necessarily a bad thing, not because DC and DP don’t get on, they do, extremely well, but living together changes the dynamic for everyone.
The one thing about your relationship which would concern me is the fact that his children are against you. This is unfortunately likely to get worse rather than better, and you don’t want to be part of a dynamic where the DC don’t come over because they don’t want anything to do with you. So while I would introduce your DP to your DD, I wouldn’t look to move in together at all until the DC are adults. Sorry.
Too many people move in together quickly and believe things will work out and then they don’t. Far better to put the children first and move in later if that is what is meant to be.