Hello - we cruised to Alaska this past summer on the Infinity - Celebrity Cruises. Although our kids are a bit older I know there were plenty of families on board with 4 year olds. A lot of the cruise lines have tailored programs and recommend certain shore excursions that are child friendly. I know speaking of the Infinity - they had a HUGE play area for kids and wonderful counselors (our kids have sailed 3 times on Celebrity and both loved the kids programs) Infinity also has alternative dining that works with fussy ones (whose kids havent been fussy from time to time). I am not sure about other cruise lines, but I know Celebrity also had childcare, including lunch, for a nominal price while at the different ports. That is an option if you want to head out on a not-child friendly excursion.
Celebrity is not generally known for their child care, but we have found they go all out for the kids and parents on any one of their ships (we cruised the Century twice and Infinity).
If you have any questions, please feel free to ask!
I'm the family cruise editor at CruiseMates.com and yes, we cruised Alaska with NCL when our daughter was 4-1/2. We had a wonderful trip and she has lots of great memories like swimming in the ship's pool with snow-capped mountains behind her! Alexandra is a great little hiker so she did plenty of active excursions with us while in port which is the best way to see Alaska. Mostly, we hiked or explored ports independently and only took one excursions sold through the line to a Native American dance show.
Alex also had fun in NCL's youth progrm and there even was a ranger talk tailored to the kids while we were in Glacier Bay.
As long as your child is energetic and willing to walk a bit in port, you should definitely take him/her to Alaska.
Luisa Frey Gaynor