Hi Twin Mama:
If you're willing to drag a lot of gear along with you, then by all means go on the Alaskan cruise. I'm the family cruise editor here and my 9 year old has been on 13 cruises and my toddler has been on cruises at 7 and 9 months and also recently at 18 months. You should read the article on this site I wrote called "Taking the BAby" about hints on what to pack and expect.
Make sure you also get a cabin that is big enough to fit two cribs in. We recently were in a triple cabin and there wasn't enough room to open the couch/bed for my older child to sleep on while setting up the crib at the same time.
Frankly, the travel days to/from the ship will be a bit crazy with two little ones. However, cruise ships are great places for kids that age for a few reasons: they love toddling/strolling around looking at all the indoor and outdoor scenery; crew and staff are usually very helpful and happy to see babies on board; you can even get a cabin with a balcony so that when the babies nap you can sit outside and enjoy the beautiful scenery. Also, with a husband and mother along, you can take turns going to entertainment at night and also exploring ports by day. Most of the ports are not huge so you can stroll the twins around. However, I found the best way to explore Alaska with kids is with a baby backpack -- there are a few easy hikes right in walking distance of the ports.
Let me know what you decide.
Smooth sailing,
Luisa Frey Gaynor