Ken Graham has a great deal of useful information in his answer, which I will not repeat. But the OP has specifically asked how to deal with a rabid animal's carcass when he is out hunting. However, the OP has not specified how populated the area is, or whether the hunter is alone or with companions.
The most important instructions are do nots: do not touch the carcass and do not let your dog(s) get at it. The next most important: report it.
I am going to try to simplify and shorten my answer.
The bottom line is that you, yourself, may not be able to do anything with the corpse. You probably don't have the heavy plastic bags you need to double bag it and carry it out safely even a short distance, nor a shovel to bury it the recommended four feet deep, nor anything to safely manipulate it into a bag (e.g., a shovel). You may not even have heavy duty work gloves with you. As for burning it -- no. The policy quoted in Ken Graham's answer is overkill for a single carcass, but it should give you pause.
You help nobody by exposing yourself to rabies.
Your responsibility is to report it and, to the best of your ability, guard against others stumbling upon the carcass, for example domestic animals or children.
Thus, after making sure your dogs will not get at it, report it. Your first choice is Animal Control. Other possibilities are the local game warden, the owner of the land or the agency managing the land or the police.
I am now going to assume that you are not in the middle of nowhere, but in a rural area and not far from your car or from other people (e.g., a farmhouse). If you can get through to none of the responsible agencies, and if you have a companion, one of you walks out to report in person, and the other stays to make sure no one stumbles upon the carcass.
If you are alone, and have gotten only recorded messages telling you to leave a message, then, after waiting a reasonable time for a call-back, as a last resort call 911. (The recorded message might well happen with Animal Control, owners and wardens, but I'd be unhappy if it happened with the police.) It's better not to leave the carcass unattended if there is a significant chance that a domestic animal or a child will happen by.
If you are in the middle of nowhere, report the carcass when you get out. Whatever burying you can do is likely to be ineffective. If the vultures are gathering, let them have it. They can eat rabid carcasses with no ill effect.
It's tempting to think of hauling it out. Think. Can you securely double bag the carcass without touching it? Can you haul it out without touching it? If the answer is "maybe not", don't try. You also have to worry about fleas.
Footnote: In a carcass, the virus can persist for days. Science Direct. The isolated virus degrades more quickly.
These findings suggest the persistence of infectious rabies virus in
carcasses left for 18 days at cold temperatures (4 °C) and up to 3
days in temperatures reaching 35 °C.