Welcome to the site.  You do sound like you have a lot on your plate.

First of all, your stepchild is not your responsibility to raise.. she has two parents correct?  It is their role.  If you live together, you will obviously interract.. and may have authority in your home.. but again, not really your job to be her caregiver and discipline and oversight is her father's job.

Second, It is not necessarily natural to care for another's offspring.. the offspring of another female.. it is just at odds with our biology.. so you have to work at overcoming a probably natural feeling that it's not right.  throw in the mix of BM's and lazy or incompetent bio father's.. it can be a tough row to hoe.

Third, if you really have mental health struggles.. you need to work on caring for yourself first.. just like they tell you in the airline safety talk.. put your mask on before assisting others.  

Fourth, please try to resist the urge to add a child of your own to this mix.. if you think you are overwhelmed now? add pregnancy hormones and another screaming resident to your household.  Think long and hard about whether this is the right relationship before you jump in and overcomplicate things... there are red flags you should be looking hard into at the moment.. and having a child is not going to be a solution.

I think your right to have concerns.. and don't blame you for feeling overwhelmed.. please try to get yourself some counseling.. it is an absolute need for you.. it's self care you should not put off.  Really look at your BF's ability to parent his child.. is he looking to you to do it because you are "the woman".. that is a huge problem if he is.

Tell us more about your role in this little girl's life and how your partner parents. Frequently we find that the biodad pushes childcare responsibility to the stepmom, but then doesn't support the stepmom either and instead takes the child's side, or pampers the child while ignoring his partner, or even blames the partner for whatever has gone wrong. Frequently the problem isn't the child at all, but the lack of parenting by the actual parent.

But, whatever the reason, you are overwhelmed and can't continue as you are. It's NOT selfish to take care of yourself--it's required.  If your sister or best friend or even a client were in this situation and feeling the way you do, what you would tell them?

I try very hard to keep my focus on my husband when I had those types of feelings. Kids are just kids, once they get older this changes but at 5 she's just a kid. 

Any issues you have are due to your husband. A stepparent doesn't just invite herself into a family. The bioparent needs to make a space for you and facilitate a relationship with his kid. It won't just happen on it's own because he puts you in the same space. He should also insulate you from any drama his ex may cause and not push you into a role you aren't comfortable with. He should also be in charge of discipline or any difficult parenting. 

The best way to have a good relationship with a stepkid is if you both take your time, get to know each other, and you have the freedom to do fun things. Kids don't like stepparents that show up and are pushed into a parental role too quickly.