My heart breaks for your little girl.
Please keep her going to counseling. Maybe she needs time to open up to this person, or maybe this counselor isn't the right fit. However, considering that one of her parents has completely rejected her (does she know this?), it will take time for her to be able to trust another person and to open up. She may be very afraid of saying the wrong thing. She may be afraid that anything she tells the counselor could upset you... there are a lot of 'ifs' in a kid's head.
What might be helpful is the great book on communication "How to Talk So Kids Will Listen...And How to Listen So Kids Will Talk" by Faber and Mazlish. This book does not deal directly with abandonment, however, it does discuss empathetic listening techniques, which is a lot of what you want to be doing when/if the subject of her father comes up.
I would go the middle route, which is to say I wouldn't throw him under the bus, nor would I defend the man. There's an old saying "Shame the parent, shame the child"; whether or not she is having a relationship with him, she is still his kid, and hearing what's worst about one's parent can cut deeply. I would instead offer reflective and empathetic language; when she says "he's a jerk" you can say "Yeah, I can see why you feel that way. He's really disappointed you". In this way, you validate *her* feelings without dumping on him more than she can deal with.
Kids also shut down a bit to protect themselves. I have my own history with being abandoned by my father, and without going into details, a lot of what I did was self-protection. This may mean that she will get mad and blame you or herself for dad not being there. She may still want to protect him, in order to protect herself. She is still very, very young.
Young girls get so much of their self-esteem and self-identity from their fathers, and yet, be careful with any men who would befriend her or show her attention. I agree that having good experiences with other men is important, however, you have to remember that they will need to be of some pretty upstanding moral caliber AND that she will need them to stick around for a while, or it's just a re-run of what's already happened for her. The other concern at this age is that sometimes crushes may develop due to positive attention being paid to young women. They're just kids and have a hard time sussing some of this stuff out. Other than uncles, grandparents, or beloved family members, I would also look into constructive group activities. If you belong to a church, get her plugged into the tween/teen activities. If you don't, consider talking to the counselor and asking for suggestions. There's a lot of stress at this age on both fitting in and boy/girl romantic relationships as well as friendships, so this can be a very confusing time. Focusing on local nature camps, healthy activities with peers-- let her pursue something she might love, like acting or a sport or whatever else interests her. I would focus less on finding a dad-substitute and more on giving her ways to gain social acceptance just for who she is. And again, the counselor might have some good suggestions.
Best wishes. I hope that somewhere down the line, there is healing for you all.