Since you are married, your best option is to file a joint return. Head of household status is generally available only to a single person (or a married person separated from their spouse for the latter half of the year) raising a child. Even if you did qualify for HOH status, she would be considered "married filing separately"; if she gets SSDI then 50 to 85% of her SS check would be taxable under that status. (SSI, the other option for low-income disabled people, is not taxable.)
Though in MOST cases persons receiving only Social Security (including SSDI) don't need to file, that is NOT always the case. As I suggested above, married persons filing separate returns are generally taxed on at least 50% of their total SS check regardless of amount, possibly up to 85% depending on amount and other income. Also, in some cases lump-sum SSDI payments may be big enough in and of themselves to trigger SS taxation. If not sure, complete IRS Notice 703 on the back of your wife's SSA-1099 to see if she may need to file.
