
Sue! It IS The Dreaming Jewels! I remember the doll, Junky, and the female dwarf! Wow, thank you!

The password is "fuzzbuzz" or "fuzzbizz"

No, definitely not. It was a mass-market paperback, earlier than 1989 I would say.
Ann aka Iftcan wrote: "you sure it was an island? Sounds a tiny bit like My Side of the Mountain or possibly one of the other books (there are 3 in the series.)"I won't rule it out, but I really thought there was a water crossing involved - and him hiding his boat. Maybe I'm blending two stories together...

I only remember a boy, but the island was in a lake.

Wow, thank you! Sometimes I wonder if these things are all in my imagination, but my mom worked a the library and I remember reading this over and over.

Seems the main character was a girl pig that wore a dress.

No, I know it's not a lot to go on.
Amber wrote: "This sounds like Dorothy Daniels The House on Circus Hill."Nope, but thank you! I wish I had more to go on...I know I'll recognize the name if I hear it.

I remember that he has to sneak back home for supplies.

This book is probably super trashy but I remember being fascinated by it.

How about
The White by Deborah Larsen? This is another fictional account of Mary Jemison.