Are you using the magical express to get to your hotel? If so, I would say yes, get your own luggage. I don't think you will have to wait until the next morning, but it will take them a couple of hours to have it delivered to your room (I am assuming you are staying at a Disney Resort). Last year we had a late flight like you and didn't get our bags delivered until after 11pm. Not complaining - next time we will just grab them ourselves if we arrive that late
We are arriving at 11 pm at MCO and are letting DME handle our luggage. We have 3 young children and I would rather be awakened a couple hours later at the resort than have to handle our own luggage. We are just going to make sure we have all of our jammies and personal essentials in our carryons.