Yeah,

surely you don't need to cancel your Qatari visa at all. Because, you can have risidence card for Qatar and Bahrain or UAE or Saudi Arabia at the same time. I know couple of guys who have residence cards of Saudi Arabia, at the same time, they have a residence card of Qatari. Actually, one doesn't affect the other at all.

Just go for it and if you want to renew the Qatar residence card afterwards before it expires, you can do that and keep both valid.

Good luck,
Bonne chance,

Cheers!