Possible to get visit visa for mother, provided you have your family here in Doha.
If not you can get a tourist visa in some hotel or travel agents like Cleopatra, etc.

Documents required for visit visa:
1. sponsor NOC/letter.
2. Filled in form, link:
http://www.moi.gov.qa/site/english/departments/PassportDept/resources/20...
http://www.moi.gov.qa/site/english/departments/PassportDept/news/2011/03...
3. Passport and Visa copy of both you and your wife.
4. Passport copy of your mother. (The names should match in yours and your mother passport)

(As she is 60+, they might just ask you to get a signature from the senior inspector/mudeer there, and they normally do it for you... just be polite (you may be already :))
Apply in any MOI in musaimeer, madina khalifa, wakra, etc.

For Tourist Visa, you probably need only the passport xerox of your mom. She might have to show cash upto 1750 US dollars before boarding, in case of tourist visa.

Its nice, I congratulate you for trying for you mother and bring her here and getting an opportunity to serve her. All the best.

Islam and status of mothers:
The mother has many major rights over her child. These rights are innumerable, but we may mention the following:
(a) Love and respect, as much as possible, because she is the most deserving of people of her son’s good companionship.

Abu Hurayrah (may Allaah be pleased with him) said: “A man came to the Messenger of Allaah (peace and blessings of Allaah be upon him) and said, ‘O Messenger of Allaah, who among the people is most deserving of my good companionship?’ He said, ‘Your mother.’ The man asked, ‘Then who?’ He said, ‘Your mother.’ He asked, then who?’ He said, ‘Your mother.’ He asked, ‘Then who?’ He said, ‘Your father.’”

She is the one who made her womb a vessel for you and nourished you from her breast. You have no option but to love her. The fitrah (natural inclination of man) calls you to love her. Love between mothers and children and children and mothers is something that Allaah has instilled even in animals, so it is even more befitting for the children of human beings, and for Muslims in particular.

Allaah says (interpretation of the meaning):

“And We have enjoined on man to be dutiful and kind to his parents. His mother bears him with hardship. And she brings him forth with hardship…” [al-Ahqaaf 46:15]

Read more here please:
http://www.islamqa.com/en/ref/5053/

Thanks!