The Girl of Ink & Stars by Kiran Millwood Hargrave

Forbidden to leave her island, Isabella dreams of the faraway lands her father once mapped. When her closest friend disappears into the island's Forgotten Territories, she volunteers to guide the search. As a cartographer's daughter, she's equipped with elaborate maps and knowledge of the stars, and is eager to navigate the island's mysterious heart. But the world beyond the walls is a monster-filled wasteland - and beneath the dry rivers and smoking mountains, a legendary fire demon is stirring from its sleep. Soon, following her map, her heart and an ancient myth, Isabella discovers the true end of her journey: to save the island itself. Originally published as THE CARTOGRAPHER'S DAUGHTER, this is a enchanting novel by an author the London Times called "[r]eminiscent of fantasy greats such as Philip Pullman and Neil Gaiman."