I am looking for a book about a girl who fights a war after her father dies. She forms an alliance with vampires and werewolves and other creatures. The opposition believes in science. She wins the war.
Could this be The Cry of the Icemark?
The Icemark is a kingdom in grave danger. Its king has been killed in battle, its enemy lies in wait, and its fate rests on the shoulders of one girl. Thirrin Freer Strong-in-the-Arm Lindenshield, a beautiful princess and an intrepid warrior, must find a way to protect her land from a terrible invasion. She will forge an extraordinary alliance of noble Snow Leopards, ancient Vampires, and ferocious Wolf-folk. She will find unexpected strength in her friendship with a young warlock. And she will lead her allies to victory with her fierce battle cry: "Blood! Blast! And Fire!"
From the Wikipedia entry, note of the empire being science-based:
Thirrin, having just made an alliance with the werewolves by saving their king, must now seek out more allies, as the Icemark and the werewolves alone cannot defeat the Empire. Although they have the support of their vassal, the Hypolitan, more are needed. Thirrin, with the aid of a young warlock, Oskan Witch's Son, must attempt to win over the Vampire King and Queen. They know this will be difficult because of the centuries of distrust and hatred between the two races. Because the Empire hates all that is unscientific and irrational, the Vampires know that if the Icemark falls, the Empire will wipe out the Vampires next. With this in mind, the Vampires reluctantly agree to send aid.
Found by searching for medieval fantasy novel redheaded girl allies with vampires and werewolves against science