Decathlon rock shoes are good value, but for your purposes, trainers are probably fine. They grow out of them before they are anywhere near worn out.We had an Edelrid Fraggle XXS which is a good harness, but has an odd extra elastic piece between the leg loops which seems to serve no purpose other than to make it fold up and wedge up their bum, I cut it off. We've had both kids in it since age 4 or so, my daughter in now 8 and it's just getting too small for her, but she's ready for a sit harness now.
I've been a fucking idiot and referred to the north west lakes. I meant north east! We stay near the north end of Thirlmere.
We found that outdoors it's better to do routes you can walk off from if possible to avoid scary lowering off. We usually opt for me belaying at the top (esp if trad setup) and wife getting kids them ready at the bottom. a friendly and encouraging face at both ends of the climb.
Sounds like she'll remember it in a similar way.
how much variation there is between children in how fearless/cautious they are.