Will my daughter receive a monthly check if her father is on permanent disability?

Are you asking about Social Security disability payments? SS Disability payments go to the "insured" person (the disabled person with the work experience) and possibly his/her spouse and children. The amount for the child is generally 1/2 of the disabled worker's benefit amount, until he reaches age 18(or through age 19 if the child is a full-time student), although there is a cap on the total payments available to a family unit.

See: Benefits for People with Disabilities