There are different ways to view the world to come. Will there still be natural disasters and dangerous animals? That's necessary to the balance of nature as we understand it. If so, how will the saints be safe? If not, that will be an unrecognizably different kind of world.
One possibility, which I've discussed before, is God's providential protection. But here's another possibility: in Scripture, some prophets and apostles have the ability to perform miracles. In principle, the saints in the world to come could have the same abilities. That would enable them to ward off dangerous animals or ward off natural disasters. Or in some cases they might have the prophetic foreknowledge or counterfactual knowledge to dodge impending threats.