Who issues the disability checks? If these are SSDI, they won't count as taxable income unless she had to file MFS, so that's not an issue.
However, according to you she gets $3000+ a year. Your spending would have to outspend hers. This includes money from her savings. There is a support test in irs pub 501.
If you *do* qualify to claim her, yes, then you could claim HOH.