L.B.
You've had some good ideas so here's my take on it. I would recommend getting involved in some school program (although it may be a little late in the season for it now) but certainly come fall! Then I would make an overture to do something special for your daughter. Plan a "Just because" party. Make this an EVENT for your daughter and plan something really cool like a scavenger hunt, make over party, tea & doll party, or go someplace cool like a bounce house/activity center. If your daughter doesn't give you the names of the girls she's playing with, check with the teacher and get the parents names and numbers. THEN, in addition to the invitation you extend, I would follow up with a phone call to each one of them personally letting them know why you are doing this and how difficult you have found it to get involved and find play mates for your daughter. Perhaps this will open up avenues you never knew about. Many times we just rush in and rush out of school. I have to say I only know one parent in my son's class fairly well and none in my daughters and I am a SAHM and volunteer on a REGULAR basis at the school! Some people just aren't that social! We invitied 18 people to my daughter's birthday party 2 months ago and only got 6 to come. Likewise with my son, only 3 came. People are busy and wrapped up in their own lives. I commend you as a parent who is empathsizing with her daughter about a difficult time. I hope I've given you some ideas. But I really think, ultimately, it will be your taking the bull by the horns that will get anything done.
BTW- at the party, I would chat with the parents about what activities they are signing their daughters up for this summer. A lot of places have already started enrollment and it would give her something more to talk about at school and plan with her friend. Maybe you all could share car pool or you will have a contact that can pick up your daughter in case she gets sick and you can't pick her up. Always good to have a backup contact! ;)