No, you can't just assume a birth rate, however plausible. The problem says one offspring per ten years. If there's 1 in a million per generation, then there are 100 generations in 1000 years, then you have 100 mutations per individual in 1000 years, or 2,400,000 mutations in the total gene pool. That's small compared to the mammalian genome, so two successive mutations at the same site can be neglected.
It's a sloppily designed problem though.
Let's just say the prof is not one of my son's favorite...he's taking the Bio class to finish out his general ed requirements (you have to have science in both disciplines and up until now, he had not taken any science classes on this side of the aisle.)