She would qualify for SSI, which is a bit different from SSDI. SSI is based on financial need (but you still have to be qualified as disabled to get it, just like SSDI. You apply to the same place, the SSA--Social Security Administration).

As far as taxes go, the best thing to do would be to call a tax professional and find out. And call SS to verify this, but if you are providing for her, I believe it is counted as "income" and would reduce the amount of SSI she would receive, if any. If she gets SSI, she should automatically qualify for Medicaid.