My 8 year old gets social security. Do I claim the income on my return or do I file a separate one for her?

it is separate from your return.

if that is her only income and there was no voluntary tax  withholding on her 1099-SSA, there is no requirement for her to file. 

Social security payments to children.

 If the Social Security (SS) payments, including SS disability, were under his/her SS number (as they usually are), it does not get reported on your return. If it does need to be reported, it would go on his/her individual return. If that was his/her only income, it does not get reported at all. She does not need to file a tax return. 

SS is only taxable & reportable when added to sufficient other income. Social security only  becomes taxable, when his income, including 1/2 his social security, reaches $25,000