To answer the question you can eat it as soon as you can get a bite in your mouth. I would sugest a quick gut job and rinse out and hang with the body cavity propped open to cool off. I live in Northern climate so this can usually be done without too much headache. Once the body is cool go at it. Heck I know a couple guys that will be eating it as we cut it up. My self I like sliding it across the grill for a minute or two first. Of course all health regs will tell you to cook it to an internal temp of 160 to be completely safe. I would rather take my chances with dying than eating overcooked venison.

Up here our regular is to gut rinse and hang to cool asap. We leave the hide on to keep it from drying out. In southern temps the hide will have to go. We hang for a day or two or three depending on temps and time to butcher. 99% of people can not age meat the correct way to make any difference and 99% of deer do not need to be aged anyway. If you have meat taste issues your better off spending extra effort of quick cooling and clean and neat butchering practices. Contamination of meat while butchering be it hair or dirt or worse can make your meal not fit for the dogs. You can add bone meal to that list of contaminates also. That makes the meat just nasty. Bone your dear out.

Hope that helps.