Seems to me you have 30 days to get a drivers license in Ohio after moving there:
https://www.bmv.ohio.gov/new-to-ohio.aspx
"New Ohio Residents
Welcome to Ohio! You are considered an Ohio resident once you:
Take a job,
Sign a lease,
Buy a home, or
Enroll children in school
Within 30 days of establishing residency, you are responsible for transferring your out-of-state driver license or ID card, vehicle title, and vehicle registration to Ohio."
Here is an old thread discussing Ohio DL and Canadians. It seems Ohio has no direct exchange program as do some states.