I'm in a heterosexual couple, too, so no advice specific to that, but I that I'd build on what the PP said.
I've found that it's best to start of as friends and build a relationship on that level first. Be an observer of the relationship between your Partner and her DD and your Partner's parenting style. As much as you may disagree, at least early on, it's best to just fall into form with what's already being done.
Get to the point where the daughter feels comfortable and safe with you and slowly add in things a mother would do. Offer to get dress her, bathe her, make her food for her, tuck her in bed with your Partner.... Gradually is best IMO. And I've found that children will fall in love with you just by you providing care for them. The first time my DSS (2 years old) told me he loved me was when I was getting him dressed for the first time. It was a great moment.
Relax and follow your Intuition. Remember that you're all learning together.
(BTW, my DSS's mother is with a woman but I don't know enough about the relationship to offer any advice there.)