Schooling

I'm thinking about a new schooling option for my daughter.  She's learning well.  She loves to writing, reading and math and does them all for fun during her own free time at home.  So the education part isn't the problem.  It's the social part.  She plays alone at recess.  She says she's okay with it.  But I'm not. 

So here's the thing.  Am I projecting my own social needs onto her?  Does playing alone at recess freak me out because that would be bad for me, but maybe it's okay for her.

While that could be true, that doesn't seem right to me.  Even introverts need social skills and recess is the time of day for her to be working on her social skills.  Now is the time to make all those mistakes and learn from them.  My husband (who is an introvert) is worried about her labeling herself as a loner.  We don't want that for her.  She has one friend that she hangs out with on Tuesday afternoons and other than that her friendships have dipped down to nothing since she started full-time school.  This isn't good and I know it, but I don't know how to fix it either. 

I'm not working much anymore, but the work I am doing pays for my son's pre-school (which is an amazing Montessori school!  He's thriving there.  Painting, playing, learning, reading.  Amazing!) and it pays for the few date nights that my husband and I get to go on.  I'm not willing to give up either of those things.

But I'm worried something needs to be done now.  Not next fall.  But what?