I dated as a single parent and later got married. All worked out well.
The only thing I would say is that you have to take it a lot slower than you would any relationship pre kids.
When there aren't kids involved, then you can do whatever you like with a relationship really, the only people who will be hurt if it doesn't work out - are you and your partner. And that's OK because you're both adults and probably if you break up, then it's for the reason that the relationship isn't working.
With kids it's more complicated. If they have developed a relationship with someone in a quasi-parental role, particularly when there are complicated feelings about their biological dad, and then you split up it's so hugely disruptive for them because you're essentially severing a primary attachment. This is more of a problem the younger they are. So the first thing to protect against is a new partner settling into a quasi-parental role too early in the relationship - you need to be really sure that you're in the relationship for the long haul before you get anywhere close to this.
Pre kids, you can move in together as a kind of "trial run" for marriage - but if you have kids, then you can't move in together without that relationship becoming quasi-parental if it is not already. So again you need to be sure. I would actually if I could go back, my rule of thumb would be that if I was not ready to marry someone, I wouldn't move them in. DH did move in too early and it was great at first but then became an issue and I think we probably would have split up except that totally by chance, he got the option to take a job he really wanted in another city and I said go for it - if we're meant to be, we'll stay together. We did, spent a bit over a year being long-distance and then I moved with DC to be with him, and the timing was right at that point.
And the other thing to be aware of is whether the kids are actually comfortable with your new partner. Sometimes they don't feel comfortable with them for whatever reason. So it's a bit of a delicate balance, I would definitely try to keep them totally separate for a while, so you can screen out any obvious dealbreakers/red flags. Once you're fairly sure that things are stable, then introduce them but in a very casual way like he is a "friend" and on neutral territory.
If you are getting close to the point of moving in together then you can trial it (a bit) by doing extended weekend stay overs, holidays together etc.