No, elementary schools would not issue Form 1099-Q. I think you may be thinking of the schools issuing Form 1098-T for tuition. Your qualified tuition program would be where to get Form 1099-Q. By definition, the elementary tuition qualifies as an education expense for grade school.
The Tax Cuts and Jobs Act: Section 529 Qualified Tuition Programs: 529 plans can allow distributions of up to $10,000 per-student to pay tuition expenses for a public, private, or religious elementary or secondary school.
From Internal Revenue Code Section 529: Treatment of elementary and secondary tuition
Any reference in this subsection to the term “qualified higher education expense” shall include a reference to expenses for tuition in connection with enrollment or attendance at an elementary or secondary public, private, or religious school.
As long as your distribution was all for tuition, there would be no penalty.
