Not saying I agree that peak oil is here yet, but if it is, I think our civilization will survive.* It might hit a rough patch, but we’re not all going to die.
Here is a good article on why we shouldn’t be too concerned: Peak Everything?
Stanford University economist Paul Romer has observed, “Every generation has perceived the limits to growth that finite resources and undesirable side effects would pose if no new recipes or ideas were discovered. And every generation has underestimated the potential for finding new recipes and ideas. We consistently fail to grasp how many ideas remain to be discovered. The difficulty is the same one we have with compounding: possibilities do not merely add up; they multiply.” The above examples show that while the production of physical supplies of resources may peak, there is no sign that human creativity is about to peak.
You should still be concerned about preparing for disasters and such, but be level-headed.