I would a) keep the kid away, but just behind a hurdle or similar, so can sniff each other but no suck, and b) if she is still quite skinny maybe put back the mating another couple of months unless you are desperate for spring kids. Any chance you can run her through on let's say once a day milking? She would slowly put on weight over the winter and then a lot more next spring & summer.
What breed are we talking about?
I am usually not keen to mate my goats every year, unless they are in danger of going overfat during the winter (on twice a day milking mind).