I have an 8 month old and a 28 month old. We just went to Florida (not a cruise) with them, and the main issue for us was not the flights, but nap times. The baby takes a morning nap, so at least one person had to go back to the room with the baby during naptime. Afternoon naps were just miserable because if one would fall asleep, the other would wake up. If the sleeping situation were easier, we'd travel more often for sure!
I'm sure safety is not an issue, especially since you will have so many other family members traveling with you. Cost depends on a lot of different factors, such as # of days, room with a view or interior, and which cruise line. You can also probably get some deals through a travel agent by booking together with your flight.
We're in Huntington, WV, and the flight to Florida was not long at all. Under 90 minutes. Kids under 2 usually fly free if they sit on your lap, but I recommend you buy a separate seat for your child and have her sit in a car seat instead of trying to have her sit still on your lap unless she is a very compliant and cuddly child. Make sure your car seat is approved for use on a plane beforehand. If you don't want to use the carseat, then just stow it under the plane with the luggage. You'll need it for the car ride to the cruise ship. The wait in the airport was long and boring, especially since our flight was delayed, so be prepared to walk around with your child because she will probably not want to sit in a seat that long. Bring her a backpack with quiet activities (magnadoodle, books, a doll, etc...) and a snack.