It's worth a net trawl searching for a frame size. I got a nice little Trek 1.2 (previous year's model) from
Evans or similar.
I'd been looking for ages and was simply not impressed by what i saw on IslaBikes' website and what I saw of their product among friends' children and in bike racks. I didn't (and still don't) get the hysteria. it reminds me a little of the enthusiasm for Cath Kidston kitchenware some years ago. Quite inexplicable yet the product and the lust for it were ubiquitous.
All 3 kids rode the baby Trek from 9-11 or 11-13 (daughter).
There can be issues with brake-level size, but not big issues. Many children have a bit of a reach issue the first time they use a certain set of levers, but this goes very quickly. It can be exagerrated by the unfamiliar layout of the bars and levers, so a non-issue can appear to be an issue. It's the same with crank length, although this Trek was on 165s, which was nice. Some retailers or manufacturers make a big deal of lever reach. Put a kid on a bike with a big reach to the levers and after two or three rides round a car park, they're totally at home. Mine were descending at speed on the Malvern Hills with a bike whose levers were (according to some child-friendly retailers) way too big for them. The main issue is geometry of frame, seat stem, bars. The adult-sized levers were fine for tiny 9-year-old hands.
On a first road bike, height difference between saddle and bars is something to consider. The bum-in-clouds riding position takes some getting used to, so you sort of morph them into it over a few weeks. Lots of sodding about with Allen Keys and much patience required of the child, but comfort is key and so is confidence. They will be chucking it into corners and whipping down the hills in no time.
The Trek I bought had 650c wheels, which I hated when I saw it, but got to love as they lent it some scale and made the ultimate transition to 700cs on a bigger frame more of a natural progression.
You will not get many years out of a road bike bought for a 9-year-old. Mine was for 3 children in succession, so there was less of a cost per user.
Bought for £390 and sold for £270, some years later. I think that was good value at slightly over £30 per child who used it.
Along the way I bought a couple of stems for it as kids grew. I still have those.
Everyone makes different choices and I may have done completely the wrong thing. But it worked for us. All the kids still ride road bikes, one of them in (fairly modest) competition.
Caution: After almost any other type of bike, a road bike is very 'darty'. It changes direction when you blink. You will no longer be aware of this if you've been on one for a while... but when you first ride one it is a stark contrast. Make sure the kids know this.