Apparently, the correct word for this is cot. Though, in a Western context, it has a slightly different form and function (from the Death and Funeral Glossary):
COT - The stretcher-like carrier used to remove deceased persons from the place of death to the funeral home.
Example of its use, from Themes and Readings for Assemblies:
I remember the hakim was concerned for the body of Teshoo Lama. He haled it out of the holy water in his hands, and there came afterwars thy horse-seller from the North with a cot and men, and they put the body on the cot and bore it up to the Sahiba's house.
Of course, the best thing would be to use whatever word the locals (the Muslims referred to in this particular instance) use--if they have a specific term for it.
For example, if you were describing the scene you could say:
The people placed the shrouded body in the tabut (a sort of metal cot for carrying the deceased to the burial site).