When Sally O'Malley Discovered the Sea — Karen Cushman

From the Newbery-Award winning author of Catherine, Called Birdy and The Midwife's Apprentice comes the story of an orphan on the American frontier who decides to go west--with nothing but gumption as her guide.

Sally O'Malley is an orphan working at a mineral spring hotel in the woods of central Oregon--that is, until she's chucked out like chewed-on chicken bones, due entirely to an unfortunate incident with a pig and some church ladies.

And so Sally decides to head west to the sea.  Glorious, she's heard. Fierce, she's heard. Why not see for herself? Before long Sally encounters a dangerous bobcat--and that's just the first day! Safe in the knowledge that she's fearless, she continues on her journey with no place to belong and no one to depend on. And that's just fine with her.

Then a lady called Major, an old donkey, a loyal dog, and an abominable brat show Sally that she's not quite as brave as she thinks.  
It turns out that counting on someone else is the scariest thing of all.