I agree with the Rattlebag recommendation. There is also a series of Lifelines books, which are anthologies compiled by a school in Ireland, with reasons for each recommendation by the person recommending.
The Rattlebag suggestion reminded me that Ted Hughes put together a collection called “By Heart” - probably has a mixture with some modern stuff - but it was designed to be read aloud and easy to recite and remember.
Sorry I read your post in full after I thought of Mary Oliver - she might not be as old as your daughter is enjoying at the moment but I think her poetry is beautiful and studied 19th century poetry - maybe she will like her. There's another American poet I'd like to recommend as well, wait there ... x
It has 1,828 poems ranging from Chaucer to Donne to Shelley to Whitman to Yeats and Auden. It's one of those things you can lose yourself in for hours and certainly introduced me to lots of poets I'd never heard of before.
In fact, I'm going to go find my copy and take it to bed.
A Poet’s Guide to Britain, edited by Owen Sheers, is a lovely anthology of poems from all around the UK, about its cities and towns, its landscape, its people, etc - lots of well known names in there. A good blend of newer and older poets.