You can not claim Head of Household (HoH) filing status without a qualifying dependent. If your daughter files a tax return, claiming a dependent of her own, she (and/or her child) cannot be your qualifying person for HoH.
So, the bigger question is should your daughter file her own tax return. The answer is No. There is nothing for her to get by doing so.
The money you hear about people getting for just filing a tax return claiming kids requires them to have some earned income (wages or self employment). Without earned income, they are not eligible for the "refundable" Earned Income Credit or Additional Child Tax Credit. Both credits are calculated on the amount of earned income you have. No earned income means no "refund". A small amount of earned income means a small refund. The child tax credit does not "kick in" unless you have at least $2500 of earned income.
A child can be the “qualifying child” dependent of any close relative in the household. It will be much better, for the family, if you claim the child, as well as your daughter.
