Yes, it is possible but I suggest you ask your company to give you a hard copy printout of the cancellation of the visa. They can do it within seconds through their computer. Make a copy of it for your files. The original document of the cancellation will be kept at the airport by the immigration people.
It is up to your company if they wish to have the company's ID back but as for the Qatar ID, the people at the immigration desk at the airport will ask you for it and you will need to hand it over to them.
I am stating the above as recently one of my colleagues was in a similar situation as yours. He went back home.