Does down syndrome qualify as a disability per tax records?

It depends on the individual.

For income tax purposes, disabled means "unable to perform substantial gainful work" due to a condition that is life-long (or will last more than one year) and is certified by a doctor.  The ability to work a minimum wage job is considered sufficient proof that a person can perform gainful work, but working in a sheltered workshop for people with disabilities is not considered gainful work.

Many people with medical "disabilities" can still perform gainful work and are not disabled for tax purposes, and of course there is great variation in the degree of impairment among persons with trisomy 21.  So it depends on your family's specific situation.

In the case of children under age 13, there is no actual tax benefit for checking the "disabled" box for a dependent.  At age 13 and older, checking the box for disabled will allow you to claim the child and dependent care credit, if you pay for care for the dependent so you can work, because the dependent can't care for themselves.