Dear Hari,

1) You cannot bring your parents on your personal sponsorship, if your wife does not hold Residence Permit in Qatar.

2) Immigration has suspended issuing airport tourist visa which is valid for 14 days and extendable up to 28 days.

Hence, only option left for you to bring your parents is through Hotel tourist visa. They can stay maximum 1 month.

If you search old posts you will get some idea about getting Hotel visa.