Yeah. cut the tree down and dig, there's coal under it but it takes about 1 1/2 minecraft days for a tree to grow, and longer for wheat to grow if you're lucky enough to get seeds from the grass... and I got 2 seeds, you need 3 for a bread.
If you stick to the island until you can make a boat, that's the more fun way to do it. There are other islands, if you have a far render distance you can see them.