I would have thought Just William was a bit old for this age but you never know!
As well as the Faraway Tree, there is the Wishing Chair series by Enid Blyton -my dd is loving those at the moment (she's 4.3).
Also Amelia Jane, the naughty doll in the nursery. DD loves the idea that her toys might come to life when she's not there and some of them might be naughty.
Jill Tomlinson - The Owl who was afraid of the Dark. And a bunch of others by her that I don't know but am hopeful will turn out to be good!
Dick King Smith - some of his for younger children I think should be suitable. (He wrote the Sheep Pig, which is what the film Babe is based on). Especially the 'Sophie' books. Some of the books, like the Sheep Pig, might have a suitable story (i'd certainly show the film to kids that age) but the actual language might be a bit much for her just yet - might be worth a look though.
The other book like that is 101 Dalmations - the story has been simplified for Disney but the original book is actually for slightly older kids, as is the sequel, 'Starlight Barking'. Well worth it though, when she's a couple of years down the line!
The Tales of Olga da Polga. I seem to remember loving these at about that age.
And yes to some of the other suggestions on here - Wind in the Willows, some of the Roald Dahl (Fantastic Mr Fox, the Magic Finger), even Winnie the Pooh if she hasn't already read them herself, and Paddington.