SSDI and SSI are NOT counted as income for tax purposes when you're filing a return with nothing but those 2 things as your sole source of income. It "may" be counted on a joint return if, like tigger said, the wage earner's income PLUS 1/2 of the SSDI receipients income meet a certain level.
Examples:
I'm disabled and single. My only source of income per month is my SSDI. I have 1 child living with me. I'm not able to file a tax return, claim my daughter, or get EIC for her because SSDI isn't "earned" income.
I'm disabled and married. My SSDI benefits and my husband's earnings combined do not meet the IRS threshhold that says my SSDI income is counted as earnings. We file a joint return, only his income is counted, we get EIC for the daughter living with us.
Hope that helps explain it.
Also... to get EIC the child has to have lived in your household for 6 months or more, not 12 (sorry tigger). If your child lived with you until August, the child was in your home for 8 months. 8 months is longer than 6 months. YOU are the only one entitled to claim the EIC for the child, regardless of where he lives now.