I would slow right down and do nothing. Sorry if that's not what you want to hear but this has red flags all over it IMO.
Firstly, in order for your partner to either be able to adopt or have parental responsibility her father would need to give permission. So that's the practical side.
Secondly, you've only been together for two years, so since she was eleven and she sees him as a dad? Really? How has that come about then? Because while I imagine that there are many preteens who would see an incoming partner as a mother/father figure, one saying she sees a partner who hasn't been in her life for the majority of it as a dad would make me wonder A, how that idea has come about, or B, whether this idea has been more or less hoped for by the parent and the incoming partner.
And the reality is that he's not her dad and has hardly been in her life any time at all. And as she's about to hit teenager status it won't be long before she's throwing "you're not my dad!" At him in the heat of an argument. Even if her dad isn't in the picture, a man can't expect to be seen as a dad to an eleven/thirteen year old if he's never been in their life before. Yes a father-figure who is involved in her life, my partner is very much involved in my DC's lives and has taken on a lot of responsibilities of his own accord when I've been able to due to situations like illness, but he could never be a dad to them because he's not been there in the formative years iyswim.
And lastly, if you allow this man to adopt your child after only two years and you split, he will have equal responsibility over the child you have brought up on your own, and could even challenge you for access, etc.
Added to which she's too old realistically to be adopted by him. It's only going to be five years until she's an adult anyway, so what's the reasoning behind him wanting to adopt her?