I find it a tough situation. I am a huge car seat advocate and a
disney cruise addict (we've gone on 3 and are planning a couple more). Some taxis will have seat belts and some won't. We've even tried multiple taxis in port. If there are no seat belts, then you need to make a parental decision on whether or not you will still do an excursion in port. It is tough because part of the reason we go on the cruises is to give our children (and us) a chance to see and visit new cultures and communities. We've brought everything from carseats, boosters, and a really bad tote n go collapsible car seat (it is small but terrible to install).
If you do bring your seat, make sure you can install it and use it correctly. It sounds so simple, but aproximately 90% of people use their carseats incorrectly. Harness needs to be tight, clip at chest level, when forward facing the straps should be at or above the shoulders (at or below for rear facing), rear facing until at least age 1, but usually in a convertible seat before this (the infant buckets will rarely last much beyond 6 to 8 months, either because of height or weight). Also, boosters need a shoulder belt to be used properly which may be more difficult to find in port (however much easier to carry). If you have a combination seat which has an integrated carseat in the form of a 5 point harness, this can be installed with a lap or lap/shoulder belt and can usually be installed on airplanes.
To the original poster, I'm sure that you are probably doing all of these things correctly, but I posted them because many more people see these threads and I don't think that information can be said often enough (at least until 100% of carseats are used correctly).
Personally, I do as many Disney excursions as possible and hope they are in a large bus. Buses keep occupants safe by different means than carseats, but they are usually actually safer than carseats/cars. However, by buses I mean LARGE busses, 10 passenger van/buses are terribly unsafe. If you do use a bus, don't keep your child on your lap, they then become your airbag (of course with an infant, you don't have much choice). Also, avoid the front rows, you need the seat in front of you to help keep you safe.