I will second Carnival, (for basic cabin size as well) but as stated earlier, any of the family-oriented lines (Princess/RoyalCaribbean/NCL) will be great for your young one - As second choice, we like NCL because of the lower prices they tend to offer in shoulder season for balcony cabins & lower additional passenger charges. The round-trip Seattle or Vancouver Itineraries also save that extra shuttle & flight to or from ANC.
Here's a link to a Travel & Leisure article.