You may already know, but Squire is from the series "Protector of the Small" - #1 First Test, #2 Page, #3 Squire, #4 Lady Knight. I also like reading books from that time period. There are so many good ones out there and it is hard to limit it to just a few! However, Here are some others that you may like:
The Edge on the Sword by Rebecca Tingle.
In ninth-century Britain, fifteen-year-old Aethelflaed, daughter of King Alfred of West Saxony, finds she must assume new responsibilities much sooner than expected when she is betrothed to Ethelred of Mercia in order to strengthen a strategic alliance against the Danes.
Bella at Midnight by Diane Stanley.
Raised by peasants, Bella discovers that she is actually the daughter of a knight and finds herself caught up in a terrible plot that will change her life and the kingdom forever.
Catherine, Called Birdy by Karen Cushman.
The thirteen-year-old daughter of an English country knight keeps a
journal in which she records the events of her life, particularly her
longing for adventures beyond the usual role of women and her efforts to avoid being married off.
Alanna : the First Adventure (Song of the Lioness series, book 1) by
Eleven-year-old Alanna, who aspires to be a knight even though she is a girl, disguises herself as a boy to become a royal page, learning many hard lessons along her path to high adventure.
The Ruins of Gorlan (The Ranger's Apprentice, book 1) by John Flanagan.
When fifteen-year-old Will is rejected by battleschool, he becomes the reluctant apprentice to the mysterious Ranger Halt, and winds up
protecting the kingdom from danger.
Blood Red Horse by K. M. Grant.
A special horse named Hosanna changes the lives of two English brothers and those around them as they fight with King Richard I against Saladin's armies during the Third Crusades.
I Am Mordred : a tale from Camelot by Nancy Springer.
When Mordred learns the identity of his father, he struggles with
feelings of hatred, but also fights the fate which determines that he
kill the good and gracious king.