L.R.
Knowing an age for the "early reader" would help. I'm figuring somewhere between K and second or third grade at the very oldest?....
Some ideas (some you've already gotten)....
American Girl historical book series. My daughter was fine reading these on her own as early as first grade but it depends on the child and the book. Also terrific to read together. Excellent way to start introducing historical settings as interesting and fun. You do not have to do the dolls etc. to read these good books! You can find them cheaper online or at second hand stores and most libraries have them all.
Pony Pals series -- three girls with ponies who face things together. Teaches without being preachy. Good even for kids who aren't really into horses. Great examples of kids working things out on their own, yet there are adult role models present too.
Nancy Drew Clue Crew is fun. Even better is the Encyclopedia Brown series. Short stories with good little mysteries to solve. Challenges the child to figure things out.
Magic Treehouse is of course popular and good. Don't forget the Magic Treehouse companion books that are non-fiction, one-topic short books about the historical periods and places where the fictional books take place.
Wayside School stories by Louis Sachar. Funny school stories. When she is older she will like anything by Andrew Clements but those are more for third-sixth graders.
I am not a Junie B. Jones fan and neither are some other moms I know. Look through them first before giving them to your daughter and see what you think. I find Junie's language and attitudes too rude and snarky for younger kids.