I am married to a widower who has two kids. My DSS was just-turned 11 when we first got together and my DSD was almost 13. They liked me ok, but had very different responses; DSD really resisted me being part of the family, whereas DSS was more like you describe - asked for me, wanted me around, came to me for comfort, talked to me.
I think you have said the right thing so far. You can't allow her to feel that she is in control of your relationship with your DP - that is not good for the relationship but also very bad for her. So - and you haven't - don't make any promises about not getting married, or about talking to her first, etc, etc....Just keep repeating what you have said - "I care about you, I want to be in your life but I'll never replace your mum."
It is very tricky, because I would guess that she quite wants you to play a mothering role in some ways. My DSS certainly did. But it is hard for them, I think, not to feel guilty about that. We know we will never replace their mums, and they know that, but it is OK for a new relationship to develop. With DSS (and DSD too, actually), there is sometimes a pull inside - you can see it - "is it ok for me to like this woman, or am i being disloyal to my mum?" So in a way, I would bet that your DP's DD is worrying as much about her own positive feelings towards you as she is about you 'trying to replace' her mum.
Time will work it out. Just keep your boundaries clear with her, and let her know what you expect from her. My feeling towards my stepkids is that I want to love them and 'mother' them as much as they are comfortable with. That has changed over time, and I expect it will continue to change - sometimes it even changes form one day to the next! So it is hard and I mess up sometimes, but I try to be consistent and be there for them when they want it, but not push. And not to make them feel responsible for whether I come or go in their lives.
hope that helps. you sound like you really care and want to get it right.