If you are not concerned about pre-existing conditions, you should be able to purchase insurance after you have paid in full (although, as PrincessShmoo pointed out, some companies may require that it be purchased at or before final payment). There may be a deadline a few days before departure, depending on the policy.
However, note that insurance typically will not cover risks that are known at the time of purchase. For example, if you buy insurance after seeing reports of a named storm forming in the area where you'll be travelling, the insurance will probably not cover cancellations or costs due to that storm. If you develop a medical condition after final payment but before purchasing insurance, it will be considered pre-existing and cancelling the cruise because of it won't be covered by most policies.
On the other hand, trip cancellation insurance has no value until you have non-refundable costs. It's certainly possible to purchase it as soon as you make a deposit, to make sure you don't forget and to help with budgeting, and purchasing at the time of the first payment is often a requirement in order to get coverage for pre-existing conditions. It's not financially necessary, though, because if you cancel before final payment you'd get a full refund from the cruise anyhow (except for concierge and some special itineraries). If you purchase insurance through
Disney Cruise when you book a cruise, it is not actually charged until you make your final payment.