You are talking about The Farthest Away Mountain by Lynne Reid Banks. I loved that book when I was in elementary school!
I also still have her book The Fairy Rebel, which is a lovely story. She is the author of The Indian in the Cupboard as well.
From the Wikipedia article:
It features a strong female protagonist who has read a lot of fantasy stories herself, and who constantly hears at night calls to her from a nearby mountain.
One morning, she wakes up early having heard someone call to her in her dreams. She looks out the window and sees the Farthest-Away Mountain nod.
Before she sets off on her adventure, a little doll she owns comes to life with a sneeze, and gives her some advice on what she'll need for her journey.
She takes out the brass statue to comfort herself with, and one of the tears she is crying lands on the little man's nose and the magic of her tears wakes him up. He finds out that she is going to the Farthest Away Mountain and tries to talk her out of the journey, but when he finds out that the Mountain called to her and nodded, he realizes that she has to go, though he doesn't explain what this means. He gives her some advice - telling her to bathe in the lithe pond, whatever that is - and also warns her about the dangers of the Mountain.
Her journey takes her across a field of spikes that she manages to pass by discovering that her tears cause the spikes to go away. She defeats a dragon assaulting her in a cabin by laughing, which scares the dragon away. She tells a story that she learned from a diary (I think) to three gargoyles who help her scale the mountain, and crosses a field of snow with checkered colors on (that would kill her in various ways) by kicking out underneath the snow.
She begins to climb up the Mountain path and is surprised to discover a gargoyle guarding the path named Og. She speaks to him and he speaks back and while at first he is quite happy to bar her from the path, when she tells him she has always thought that gargoyles were more sad than they were cruel, he is overwhelmed and agrees to help her. He sends her on to his two brothers, Vog and Zog, who aid her on her way. It is Zog that reveals the truth, that it is the Witch that makes the snow different colors, because she fears the color white.
She rescues a prince...but he turns out to be an utter bore she wants nothing to do with, and she discovers that the little doll she had all along was a prince trapped inside of a doll, frees him, and ends up with this little doll instead.
All of the master's spells are now broken, and Dakin returns to find Gog and return the Ring to the royal family, now hoping to fulfill her third goal to marry a prince. She is appalled to find, however that the prince is rather unintelligent and dull, and decides not to marry him. She takes Gog back to the mountain to reunite him with his brothers and encounters Croak - now a handsome young man once more. They marry and become the Prince and Princess of the Mountain, completing her final goal.