@SkittisH - No, coconut palm saplings don't just look like a miniature version of an adult coconut palm tree. They look like a few fronds of the coconut palm's usual leaves sticking upward out of a coconut (which is usually partially buried in the sand), because the coconut itself is the seed.
As for aging, your guess is dead-on. For a tree, especially one that's sixty to ninety feet tall (ninety is the "tall" type, sixty is the "dwarf" type), they grow really fast. A coconut palm tree takes five or six years to reach maturity and start producing coconuts. It can grow up to seventy five coconuts per year with the right conditions!