After a dog dies you really should bury it within 24 hours or right after the dog has died if possible.
If you know your dog is gonna die soon you should dig a hole before the dog actually dies so that the hole will be dug and ready for the dog to be buried in.
That way all you need to do is ensure the dog is dead and then immediately take the dog to the hole and place them in there and bury the dog.
That way the dog won't be decaying outside in your yard or in your house, garage etc.
If you can't bury the dead dog right away you should place the dog somewhere such as in a shed or garage away from other animals.
And place the dead dog into a plastic trash bag.
Then you can bury the dog in the ground.
If you cannot bury the dog then you can always place the dog into the trash can after putting it in a trash bag and the trash people will not know any different.