By "she "likes" him as well"... are you insinuating that she has a crush on him?
I think I was feeling just fine about the 'boy/girl' thing until that line. That, I would have to think long and hard about if and how I would facilitate such a friendship. I say this from my own remembered experience of boy/girl crushes at that age. Boys don't usually react well to this sort of attention. Playing pirates and imaginative play is fine, but boys generally get their "mean" on when they get any whiff of girly intentions. (I say 'generally'... not all boys are like this.) I myself had handfuls of clover smashed into my face for telling a boy I liked him. Another boy, a year later, dropped a pile of bark chips into my hair and hood on a rainy day because someone told him I liked him. These boys were completely nice up until then, by the way.
Hard call-- see if your daughter's interest in this boy lasts. I think, in that case, if you do have the playdate at someone's house, have an open-door/within earshot policy. Even at a young age, boys and girls can get into mischief with each other if given too much privacy. (sorry, it's the truth). I would actually do that sort of playdate at the park, but to each their own.
And I would suggest is talking to the mom of the girl friend and asking if you could make that playdate happen... pick the daughter up from school, take her to your place and drop her off at home. This mom might be more up for it if she didn't have to do the transportation piece of it. It's lonely for a girl to grow up without girl friends.
Just my two cents, and I'll be interested to see what others have to say.