I'm the family cruise editor at CruiseMates.com. I am an advocate of "starting them early" with traveling and cruising. At the age of 7 months we took my daughter (we live on the East Coast) to Arizona for a 10-day trip all over the state and she hasn't stopped traveling or cruising since! She's so used to being on the road that at 7 years old, she recently sat for the entire six-hour flight to California without getting out of her plane seat once!
Cruising is an easy way to travel with kids since you pack/unpack once yet get to see many different destinations. However, there are a number of factors to consider before booking an Alaska cruise with a 3 month old. The most important is the cruise line's policy towards infants. Princess Cruises -- one of the biggest cruise lines in Alaska -- states that infants must be at least six months old to cruise in Alaska. If you do find a cruise line sailing in Alaska that accepts a 3 month old, then you should also consider factors such as the plane ride to the cruise ship. I tend to feel that babies at six months old have a more established immune system and thus won't get sick from the enclosed environments on planes, whereas a 3 month old might be more prone to the less than healthy air on a plane. In addition,if you do cruise with your little one, make sure you reserve a crib for the ship at the time of your booking.
We cruised to Alaska when my daughter was 4-1/2 years old and she loved it. Since we take her hiking a lot, she was a real trooper during port days. Alaska's grandeur is so impressive that perhaps you'd rather wait until your baby is a child -- that way she can remember the beautiful sights she will see on the cruise.
As someone who has taken her daughter on 10 cruises and almost 30 extended land trips in seven years, I definitely support taking kids on the road at an early age. However, if this is your first child, be aware that traveling with babies and toddlers involves a lot of equipment (strollers, car seats, etc.) and a lot of compromise. As they mature, though, this aspect gets easier and the joys of travel are what will remain in your memory!
Good luck on your decision.
Thanks for your reply. I didn't know about the age restriction. There must be a good reason for it, so I think we will wait for next year. The problem with Alaska is that the window of opportunity is so narrow each year.
We have been traveling with our daughter since she was 3 months old. At 3 months, we took her to Paris, at 4 months to Club Med in the Bahamas, at 6 months, NYC, at 10 months Club Med Copper Mountain, at one year New Mexico. We are taking her on her first cruise next month. All I can tell you is it gets harder as they get older. On our first few trips, she was still at the age when she slept a lot so we would take her everywhere, even dinner in the evenings, and she'd peacefully sleep in her stroller while we ate undisturbed. I say GO FOR IT!! The only difficult thing is all the stuff you have to pack. Are you nursing? If you are thats a big plus- not bottles, formula, dish soap or bottle brushes to tote! I kind of consider myself a bit of a pro at this by now, so if you have any questions feel free to ask.