One, KS1 is largely consolidation for bright kids. I mean, there is new stuff, but nothing that challenged them, just that interests them.
KS2 allows the brightest to stretch themselves in terms of written projects and work. Maths is still pretty non challenging if they start y3 with a good grip of all of the multiplication tables etc, but tbh there is usually more scope for subtle differentiation in juniors.
That said, I would just keep on doing the stuff at home. She's old enough now to understand that she can differentiate for herself, both in school and out, and will be consolidating research skills (like the lemur thing) that will allow her to do that. Differentiation is less problematic as they move on from here, because they do it themselves. A basic title or project can be as involved as they want it to be.
I can honestly say that I don't think any of mine learned much in ks1, but from that point, there have been marked differences. The girls have a strong work ethic and are happy to immerse themselves in any work given, and take it to the max. Ds1 gets an 'idea' from his school work, and takes it off in his own direction (and moans about having to do the boring school work). All are extending themselves in different ways.
I'm all for sideways extension. Ime this means they are usually still working a few years ahead in their rudimentary knowledge of Maths, but they have occasionally gaps which would not be filled by grade skipping (in ds1's case it is stem and leaf plots lol) so unless you have a school which is prepared to test their knowledge of the full math curriculum for the next year, there isn't much point in pressing for a move up for math. (ds1's school have, lol. And have decided not to move him even though he scored between 80 and 100% on the next year groups end of year tests).
Honestly, infants is for playing and social skills. Juniors is when they start taking responsibility for extending their own work through school projects.