She might need to order some things online, try, and then return most of them – proper children's walking boots seem to be a bit niche, so even a big outdoor shop might not have more than a couple of styles, and the more common walking shoes or trail shoes don't tend to have the ankle support.
Scarpa do a couple children's styles that are proper walking boots, including a full leather one (currently on sale at Scarpa itself: https://www.scarpa.co.uk/products/little-terra). Scarpa are one of the narrower boot brands, though, so if she's got a short but wide foot, they might not fit.
I think Meindl and Merrell both have a children's walking boot as well, although not sure I've seen full leather, and they are wider fitting.
Or Peter Storm and Regatta do a couple of walking boots – they likely won't last as long as some of the others, but then, they're at a lower price point. I also have small feet (although larger than your daughter), and I've had a couple pairs of the Regatta children's trail shoes and thought they were good for what I paid (they go on sale regularly, and the sale often stacks with a discount code). Not tried the walking boots, though, unfortunately.