Our son's first cruise was on this ship -- he was just 11 months old at the time. He's 12 years old now, and we've returned to the ship twice more since then, and have another booked for this coming summer. IMO, it's a great ship and itinerary with an infant.
There are six general cabin types on Norwegian Majesty: inside, superior inside, oceanview, superior oceanview, mini-suite, and suite. The only two I would not suggest are the standard inside and oceanview, as they are just 108 square feet. The "superior" cabins are 140 square feet -- large enough for three, and enough floor space to set up a pack-and-play. On Norwegian Majesty, these are categories JJ, I, and II (superior inside) and EE, D, DD, C, and CC (superior oceanview). I also recommend booking a specific cabin rather than a guarantee as an upgrade on this ship can actually move you into a smaller cabin.
Happy to answer any questions.