I agreed to pay my ex-spouse a distribution from my 401k as part of our divorce agreement in 2019. Would the language in the divorce agreement qualify this as a QDRO?

A QDRO is usually specified in a divorce decree and is part of it:

 

See:

https://www.irs.gov/retirement-plans/plan-participant-employee/retirement-topics-qdro-qualified-domestic-relations-order

 

And:

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&cad=rja&uact=8&ved=2ahUKEwi_8cuPmbzqAhXMv54KHe0RBogQFjAAegQIBBAB&url=https%3A%2F%2Fwww.dol.gov%2Fsites%2Fdolgov%2Ffiles%2Febsa%2Fabout-ebsa%2Four-activities%2Fresource-center%2Fpublications%2Fqdros.pdf&usg=AOvVaw3JUD3yQSbFlfTP8l6NJgol

If the distribution was from your 401(k) paid to you and then you gave the money to your ex-spouse, it is not a distribution to an alternate payee under a QDRO, it does not qualify for that exception to any early-distribution penalty and you are the one responsible for the tax consequences of the distribution.