In normal case Qatar law does not allow to sponsor your mother. Even for visit visa they will not issue for the people above 60 years of age.

But,

If you have anyone who can help you may get visa for your mother. The concerned authority may use their discretion to issue visas in such cases. Normally for 6 months visit visa will be given using this discretion power by the concerned officer, if you are able to make him understand the situation.

Good luck!