You should be just fine with an 1145am flight.
When they assign you to a departure group (via the color coded luggage tags), make sure you are in one of the first groups to disembark the ship. If not, go to the front desk when you get the luggage tags and ask for an earlier departure group.
I travel by air all the time. Sometimes I don't check in until I get to the airport.
So, don't sweat the check-in issue.
And, as another poster stated - you will have internet access on your phone early in the morning on the day you arrive back in port. Delta will have emailed you a link to check in for your flight. Click on the link in your email and check in. Then, get your boarding passes at the airport. No worries. No worries.
Enjoy your cruise! β