There are two major airports that service Houston. Bush (IAH) is on the north side of the metro area and is about 70 miles (75 minutes) from the Galveston Cruise Pier. IAH is the airport used by many major domestic and international airlines. Hobby (HOU) is on the southeast side of Houston and is closer to Galveston. It is about 42 miles (50 minutes) from the Cruise Pier. Hobby is the home of Southwest Airlines; if you decide to use Southwest, then you will have to fly through Hobby.
Could you depart the ship and make it to an 11:30 AM flight at either airport? Well, yes. Will you make it 100% of the time? No. If you are returning to port on a weekday, the morning commute from Galveston could add several minutes to your commute time, especially if you are going all the way to IAH.
Keep in mind that in the winter months from November through February Galveston and the Houston Ship Channel is prone to fog. Ships can be delayed getting back into port anywhere from an hour or so to 24 hours. It doesn't happen frequently, but it will happen a handful of times during a season. Murphy's Law tells me that even if it only happened once next season, it would probably happen on my cruise.
Personally, for ease of mind and to avoid getting stressed out, I would not book a return flight until mid-afternoon, if not plan to spend an extra night in Galveston after the cruise.
I can't comment on what shuttle service
DCL offers to passengers flying to or from IAH or HOU. But several companies, such as Super Shuttle and ExecuCar offer transfer services to the Galveston Cruise Pier from both airports.