I took on my DH's DD as soon as we moved in together. I had no children and very little experience of them. I got dropped straight into stepmotherhood. We had her every single weekend, Friday 5pm til late Sunday, because his ex worked weekends. My DH used to go off with his mates and leave me with her. He assumed all women knew instinctively how to look after kids, a theory he abandoned after a free and frank exchange of views. 
Money was never an issue. I never resented money spent on my DSD. What idiot would marry a man who wasn't devoted to his child? How he treated her told me how he'd treat any we had, and how he'd treat me.
I'd guess if you've been in care you feel safer relying on yourself, and are anxious about depending on others. How your ex behaved will have made things even worse. I think you're being brave to allow yourself to be dependent, but it sounds as if you've got really good communication with this man, which is brilliant.
If he's anything like me, he's in love with you, wants to share his life with you, and he knows without much thought that of course your DD comes as part of the package. My DH having a pre-existing DD wasn't something that ever put me off or made me possessive about money. She's your DD, and you love her, so he will work to build a relationship with her that's his own. He's not her father, but a good SF can be hugely important to a child. The one thing that will matter to her is how stable your relationship is. It's very hard for a kid to bond with someone and then lose them shortly afterwards. I'm sure you've considered that.
One tiny note of caution. There are predatory men who target women with young children, and it's not the women they're after. But I expect - particularly with your experience - you've considered that and know him well enough to discard the caveat.