What's the Name of That Book??? discussion

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My Father's Dragon
SOLVED: Children's/YA
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SOLVED. Children's Fantasy, book about a girl rescuing a dragon on an island. [s]
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The plot of this book was that a girl went onto an island ( I think) to rescue a dragon. Before she went, she somehow got a tip from someone/ something (I forgot) to bring a lot of things including a toothbrush and toothpaste, hairties, pieces of chewing gum, and a mirror. On the island, she encounters many animals including tigers, rhinos, moneys, a lion, and lastly, a dragon. She journeys on the island, eventually getting to where the dragon was, by using tricks like giving gum to an animal ( forgot which one), tying hair ties onto the lion's mane (hence the cover), giving the toothbrush and toothpaste to the rhino to help clean their horns, and more.
When she finally finds the dragon, she frees it. The animals discover her and try to prevent her from escaping. She escapes anyways with the dragon. The monkey ( who talks with the letters switched sometimes) says something along the lines of " Give us back our dragon! We need it!". The girl flies back to her home on the dragon.
And I think this was book one of a series. I think the second book's title has the word "blue" in it, probably unlikely.