They will accept no "proof" - as in a doctor's note. It's on you to be honest about it. If you lie, and something happens, they're not responsible.
From the
DCL website, here's the Terms & Conditions that you agree to when you book your cruise:
Women who have entered their 24th week of pregnancy as of their embarkation date or who will enter their 24th week of pregnancy during the cruise will be refused passage due to safety concerns. Neither a physician's medical statement nor a waiver of liability will be accepted. In addition, Disney Cruise Line cannot be held responsible or liable for any complications relating to pregnancy at any stage.
https://disneycruise.disney.go.com/contracts-terms-safety/terms-conditions/united-states/