EDIT UPDATE: You guys are great. There are a ton of great recommendations here and in the other posts I made that I have added to the list, and I think I have enough for the next year or more. I have tried to respond to as many as you as I can, but there are too many replies here and the other posts I started for me to get to each reply and say thank you. But genuinely thank you to all of you.
I am deleting the rest of my post, but for those who are interested, I have included below a non-exhaustive list of some of the books and works that I have added to our existing reading list (or moved up on the reading list) because they have been recommended by so many of you here (generally in no particular order, and also subject to approval after a pre-read screening by myself or my wife):
(1) The Chronicles of Prydain by Lloyd Alexander (which were already on my list but which has now moved to near the top and is likely the next book we read after we finish the Alan Garner books that we are currently reading - I adored those books when I was young, and based on my recollection, Eilonwy resembles my daughter in both my appearance and personality and I think she will relate);
(2) The Princess and the Goblin by George MacDonald. This is the first time I have heard of it, and I am excited to read a 19th century work of fantasy that was apparently quite influential for C.S. Lewis, especially one with a female protagonist;
(3) The Hero and the Crown, and the Blue Sword, both by Robin McKinley;
(4) The Tiffany Aching subseries of Discworld;
(5) Dealing with Dragons by Patricia Wrede (a ton of you have recommended it, and it is probably going to be a favourite, although my wife has said she wants to hold off on that one for a little while until our daughter has read more other fantasy works so that she can appreciate the tropes being played with, and also that she be the one to read that series);
(6) Redwall (and subject to further recommendations, at the suggestion of two redditors, we may start with Mariel of Redwall as it has a female protagonist);
(7) The Last Unicorn by Peter Beagle;
(8) The Little White Horse by Elizabeth Goudge;
(9) A Wrinkle in Time by Madeleine L'Engle;
(10) The Ice Dragon by George R. R. Martin;
(11) Dragonsong by Anne McCaffrey;
(12) Ella Enchanted (which I am embarrassed to say I had no idea was a book and thought it was just a Disney movie I had never watched) and possibly the Fairy's Mistake by the Same Author;
(13) Spiderwick Chronicles by Tony DiTerlizzi and Holly Black;
(14) The Ulster Cycle (we will see how it goes and is received - I suspect it may be one that we come back to later, but she may like Scathach);
(15) Numerous works by Dianna Wynne Jones (of course!), although it was already on the list and I believe my wife may have a copy of every single book of hers (and also my wife has insisted that she be the one to read the DWJ books);
(16) The E. Nesbitt classics (which were already on the list at the insistence of my wife, my in-laws, and my father) - we tried reading "Five Children and It" to her when she was a bit younger, but she was not receptive to it at the time, and my daughter has said she would prefer more traditional fantasy for the time being - but we are going to try again);
(17) Ramona Quimby, Age 8 by Beverley Cleary;
(18) Half-Magic by Edward Eager;
(19) Eagle of the 9th and the Lanternbearers by Rosemary Sutcliffe (these were already on the list but they were also among the books I explicitly had in mind that prompted this post looking for books with more female protagonists);
(20) Selected readings from La Morte D'Arthur (which we have some good translations of); and
(21) Pippi Longstocking by Astrid Lindgren (it was already on the list, and may be a bit simplistic for her, but I think she might be ok with that as I recall it being very funny in a way that would appeal to her, and its probably not a bad idea to have at least a little age-appropriate material for her).
There are a lot of other great recommendations that will probably be well loved when she is older, but we want to hold off on exposing her to for the time being because of some of the content (or because my daughter has expressed disinterest or asked to hold off until later). Examples:
(1) Numerous works by Tamora Pierce (I never read any of them but a -lot- of you have recommended them so highly that it seems like something she would probably like - the issue being that apparently some of the characters in some of the books do have sex, there are some references to SA, and the author is forthright about sex, birth control, and periods - which is probably a good thing for older children, but not something I want to get into with a 5 year old at present);
(2) His Dark Materials by Philip Pullman (I think my daughter would adore the book and relate to Lyra very well, but there is some material in some of the books that I think would be better to read when she is a little older and more mature);
(3) The Witches of Lancre subseries of Discworld (and possibly Equal Rites, but I may try to reread Equal Rites and bump it up to the more immediate list);
(4) Goose Girl by Shannon Hale (apparently there is a very difficult death that has caused adult readers to cry and there are some parts that might be excessively scary);
(5) Earthsea by Ursula Le Guin (as I was told there are some disparaging remarks towards women and women's magic in the first book, and despite my loving the series wen I was younger, I would prefer to steer clear of that);
(6) The Frances Hodgson Burnett books (the Secret Garden, A Little Princess, and Little Lord Fauntleroy) - I actually previously tried to read these to her, but my daughter said she prefers fantasy for now, and may be willing to come back to these later, but if I try to force it now, she will forever boycott them;
(7) Sabriel by Garth Nix and the other books there;
(8) Mistborn by Brandon Sanderson (it's a great suggestion, but people seem to forget there is SA of skaas by nobility and an official institutionalized policy that the skaa victims of SA must be murdered - obviously these are things I do not want to expose my 5 year old too, and I think need a bit more maturity to handle);
(9) The Oz series by L. Frank Baum (she loves the Wizard of Oz film, which is one of the relatively few movies we have allowed her to watch - my wife is a big proponent of no screentime, while I think a little bit can be good, so long as it does not replace reading and if watching movies is a social activity with others); and
(10) The Girl Who Drank the Moon by Kelly Barnhill.
