Aldi, Decathlon, Polaris, Dare2Be, Altura all places to start, depending on your budget.
Outdoorsy/running kit rather than cycling kit may be better for the winter – my kids had/have a warm pair of Altura leggings, but Ron Hill used to do kids sized leggings as well.
Decathlon skiing base layers are stupid cheap and warm for winter riding, simple windproof/showerproof jacket. Their skiing gloves – or maybe just liner gloves inside normal cycling gloves – might be useful.
Remember – she will probably have grown out of any kit by the spring.
If she is really keen, is there a kids skills course – maybe with a local cycling club – she could have a go at?
LittleMissMC has her heart set on a new helmet for Christmas. But not the one I wanted to get her….. 🙄 👿