Judging by how you stated your question, I'm assuming you're younger than 15.
No, you cant just go out and buy an island; and I doubt your parents will go along with it.
http://www.privateislandsonline.com/regi...
There is one in the creek near me about 8 inches across, I'll sell you it for $50
Considerably more than you have. You have to remember that you would need a water treatment plant and sewage as well as electric production to even make it livable.
You can probably buy one for a million dollars. However, there is no drinkable water or electricity on a bare island.
