Destined? No, but I reject the notion of destiny or fatalism or per-determination so I scrub that notion from the onset. Will mankind, or perhaps some other species that evolves here eventually find a way to colonize other planets/moons et cetra? I hope so. We have a hard parameter of about a billion years until macroscopic life probably won't be able to survive on surface of Earth any longer, so in the interest of all biological life on this planet, someone will have to transplant it elsewhere eventually.