You really need to use an autumn feed on the lawn at this time of year.
Personally, I would spray the weeds with weed killer, give the lawn a good scarifying, and sprinkle grass seed mixed with topsoil all over.
The grass seed will grow at this time of year, and should help to crowd out the weeds a bit, giving your daughter a bit easier time next year.
Weed and feed does help, but it may be worth digging out some of the more tougher weeds such as nettles and docks.
Hope this helps!

Thank you Geraniumdad, that does help a lot. I had wondered about sprinkling grass seed and topsoil. Do I need to wait until it's had its last cut before doing this though?

I dont weednfeed my lawn after the 2nd application in July, but I do apply an autumn feed in September/October after scarifing. You can still sow some seed for patching if the ground is still warm.

I'm in Aberdeenshire and just scarified and mowed my lawn this weekend with looking to add autumn feed mid week. I don't think we'll have much opportunities up here now for another cut.
I don't have a problem with weeds as such as the turf was only laid in March, but I do have quite a lot of thatch in it. So hopefully getting rid of that will let the air in about at the young grass over the winter and it'll be nice and lush next spring.