I haven't had this experience, however I have been a stepmum to my EXDP's DC, had 2DC of our own, and now single mum with 2DC having split with EXDP. I'd be delighted to meet a new DP, though not actively looking (yet!).
One of the things I found difficult to cope with as a DSM was that this third person/stranger had such a huge influence over so many aspects of my life, despite me never having met her. A large part of this was due to EXDP never standing up to her, or holding boundaries. You won't have any of these issues, the absence of which should make a new relationship smoother in that regard.
As you have no EX to co-parent with, you'll be in charge of all the big decisions regarding your DC, even if you meet a new DP. This can be both negative and positive. I suppose you'll also have to think about what role you want your new DP to have in your DC's life. This I would have an upfront conversation about, as it'll help minimise conflict down the line (although it will probably still happen!).
Another thing to consider is whether you would want more DC with a new DP, and how you see the situation playing out with you all living together. As @candlelightsatdawn mentioned, I'd be on high alert regarding his attitude to parenting (any DC), as if it's at odds with yours, life could get tricky.
Wishing you all the best on your DC journey!