No, you do not enter your child's SS benefits on your own tax return.
Do not enter the SSA1099 for your child on your own tax return. Someday if the child has other income (after school job, etc.) and is filing a tax return, for that tax year he will need to include the SSA1099 on his own return. Until then, it does not get entered anywhere.
And...if Social Security is your only income you are not required to file a tax return, either, unless you have a 1095A for marketplace health insurance. Or if you have other taxable income, you might need to file.
Who has to file?
http://www.irs.gov/uac/Do-I-Need-to-File-a-Tax-Return%3F