I could see the problem with population. Birth rates would be extremely low, and very slow, but with the amount of girls there are there shouldn't be a need for incest. If it was just
one girl, then yeah, I could see the issue.
Also agriculture and livestock is a very important thing as well, and even if they are
there(animals that is), is there a high enough supply of them to last as the population increases? If not then we'd probably resort to eating a lot of farm produce (depending on the fertility of the ground), fruits from the native trees and/or fish. The lack of certain animals would also mean there would be a lack of certain materials to make certain things. Like for example, I really doubt there will be a dairy cow/pig on a random tropical (Then again, I am not exactly positive of the climate of this island), but since this states all resources are there, lets just say there is not a high percentage of them. If they run out, that takes away meat, leather, milk, etc.
I honesty don't think we could last too many years with out some sort of importing and exporting, unless we want to risk endangering the species living on the island. There is not a definite size of the island, and what other resources there could be that could help avoid this from happening, so we might be alright. There would need to be some heavy exploration, that's for sure, because even if we have all necessary resources now, that doesn't mean they will be there forever.