In order to claim your parent, you have to provide for over half of her support for the entire year. I assume she spends her $1,200 on her support, so you would have to provide more than $1,200 monthly toward her support. This would be necessary, but depending on whether she owns her home or not, it may not be enough to show you supported her.
The IRS Pub 17 has good worksheets for you to figure out the amount you pay toward her support. Unless you have earned an average of at least $2,400 a month, it will be difficult for you to show that you provided over half of her support.
In addition to the support requirement, your mother would have to have gross income of more than $3,800 for the year. If her only income is Social Security disability, she has zero gross income. Also, your mother must not be filing a joint return with a spouse.
The fact that your mother is disabled, or that you live with her, do not change the qualifications needed for her to be your dependent.
As far as unemployment, all you can do is apply and see what happens. Each state is different as to the time you need to be employed, and amount of wages you need to have earned, etc.