Hi
As a PR, you may sponsor your mother, and your brother will be her dependent, so he will be included in her application. You need to submit the application so his age can be locked in as under 22.
Please note, in order to be eligible, you must be residing in Canada full-time.
The OP has been in Canada only a month, but s/he has to be able to meet the Low Income Cut Off figure from Canadian sources in the year before submitting the application. I some how doubt that s/he has earned enough in the past month to meet the LICO. If he turns 22 before the submission of the sponsorship, he must remain in full time studies until such time as the visa is issued. These days, probably looking at 8 years.