Reddit mentions of The Song of the Lioness Quartet: Alanna: The First Adventure / In the Hand of the Goddess / The Woman Who Rides Like a Man / Lioness Rampant

This is a good book. I had a different book; from the Baby Sitters Club series.

Also, i admit to learning a little from the series "The Song of the Lioness Quartet (Alana: The first adventure/In the Hnd of the Goddess/ The woman who rides like a man/ Lioness Rampant). Basically a coming of age story about a girl who starts out dressed as a boy because she wants to learn how to be a knight. She is basically unprepaired to become a woman, and unexpectedly has her first period and thinks she is going to die. Only thing someone may be concerned about is that she is dressed as a boy for a good part of the story (some may see this as not empowering women), but i think it helps to address gender roles. There is some romance/sex in the novel, but it is targeted to a teen audience. http://www.amazon.com/The-Song-Lioness-Quartet-Adventure/product-reviews/0375825649/ref=cm_cr_dp_see_all_btm?ie=UTF8&showViewpoints=1&sortBy=bySubmissionDateDescending

I've just been re-watching these as well :)

These aren't detective stories, but if you want strong capable heroines, I'd recommend Tamora Pierce's books, particularly:

[Tricksters] (http://www.amazon.com/Tricksters-Daughter-Lioness-Tamora-Pierce/dp/0739451456/ref=sr_1_2?s=books&ie=UTF8&qid=1334468727&sr=1-2) series

This heroine, Aly, has the most in common with Veronica (in terms of wit, slight cynicism, talents)

But also:
[The Song of the Lioness] (http://www.amazon.com/The-Song-Lioness-Quartet-Adventure/dp/0375825649) series
[The Immortals] (http://www.amazon.com/Immortals-Boxed-Wolf-Speaker-Emperor-Realms/dp/0375827005/ref=sr_1_4?s=books&ie=UTF8&qid=1334468603&sr=1-4) series
[Protector of the Small] (http://www.amazon.com/Protector-Small-First-Squire-Knight/dp/0739446983/ref=sr_1_8?s=books&ie=UTF8&qid=1334468653&sr=1-8) series