Only the most extreme anarco-libertarians would argue that protecting citizens from natural disasters is not a proper function of government.
I am not a libertarian nor am I an anarchist. But I will argue right here and now that you are wrong. Dead wrong. In no way, shape, or form is protecting citizens from a natural disaster a "function of government". Especially the federal government. I've read the U.S. Constitution several hundred thousand times now and I've yet to see
any article or section that makes natural disasters the responsibility of the federal government.
So long as a state constitution doesn't prevent it, a state, county, or city
could make protecting citizens from a natural disaster a "function" of
that level of government.
But really, charitable organizations such as the Red Cross are the solution to natural disasters.