Hypothetically, I'd dig a deep, deep hole (at least double the depth of a normal grave) in a nice, scenic spot in the woods and put the body in there, and perhaps cover it with some kind of natural caustic agent or something that would accelerate decomposition (if it wasn't too much trouble).
Next I'd partially fill in the hole (so now I'm left with a normal depth grave), kill a dog, put it's corpse in the hole and bury it.
Then I'd place rocks on top of the dog's grave (to deter scavengers), and perhaps plant some nice flowers or a bush too, to make the grave look nice. I'd also place a cross/grave marker with "Fido" carved into it on the grave, to make it obvious.
My logic is that if the police were looking for the body, they'd be able to use technology to detect any disturbed earth and easily find a normal grave, but by burying the body deep under an obvious dog grave, I'm hoping they'd find "Fido's" grave, be a bit suspicious, but when they dig it up and find the dog's corpse, they'd assume it was only a grave for a beloved pet, then fill it in and go and search somewhere else.