I know it's cute, and lovely at the moment - but having seen what we did with difficult child 1, I would be encouraging the friendship but nothing much more at the moment. Girls mature faster than boys and if they are too involved in each other now, when they both (especially your son) need to do a lot more growing up, then there could be problems when they each separately get to the point where they develop a bit further. It can be sticky if they're romantically involved at that point.
Without the GFGness, we saw this with easy child & BF1 - they broke up twice. Each time it was at a crisis point in their individual development. While in their case they DID get back together - twice - they are both very easy child and this made it much more likely. But despite being easy child, they were both each devastated by each break-up.
When difficult child 1 broke up with his first girlfriend, it was even worse. He really didn't cope. They had got together when they were 13, she chased him because he really was too socially inept to do so. They DID stay together for two years which at that age is remarkable, but I am sad that they weren't able to have tat wonderful relationship when they were both a bit older.
The relationship broke up because she was maturing faster than he was. As part of his Asperger's, he has been much slower to mature than boys usually do anyway, which is very slow when you realise that boys in general are slower to mature than girls. He was very bitter and although the girl did try to keep the break-up as amicable as possible (she really did care about him as a friend, too) difficult child 1 was very nasty to her.
I wouldn't want to see the good friendship between your difficult child and his friend to be cut short and not allowed to continue into a good lifelong relationship, because of similar problems likely to happen over the next few years. If they stay friends, that is great - but if they become boyfriend/girlfriend too soon, that greatly reduces the chance of this.
One very positive thing though, that this says about your difficult child now - if he is such a desirable proposition that this girl is prepared to chase him and work with him like this, then whatever happens now, one day he is highly likely to be in a happy, long-term stable relationship.
Marg