Hi Megan:
Glad to hear you're taking your kid(s) on a cruise. I wasn't sure if you have other children in addition to your toddler. Unfortunately, you can't take your 15 month old into the youth room even if you'll be there too. However, you can reserve a babysitter on Royal Caribbean and pay an hourly rate. We have done this in the past and the sitters are usually very lovely young ladies. (The last one got my toddler to sleep faster than we do!) As for seasickness, you may want to try seabands. You can buy them in the cruise ship's store and put them around your/your child's wrists. However, a toddler may try to pull them off... Luckily my toddler has been on 4 cruises and hasn't been seasick yet. My 10 year old has been on 14 cruises and only got sick once. Alaska is generally a pretty mellow sailing region.
As for jet lag, be prepared to get woken up early by your toddler. We just returned from Hawaii (and spent two days prior to that in San Francisco). We are from the East Coast and thus our toddler was up at 5 a.m. most days! At least on a ship, there are plenty of public areas to walk around at that hour. We bought a portable DVD player which helped out in the wee hours of the morning! Lastly, make sure you bring swim diapers so you can bring your toddler into the splash pool if the weather is warm enough. (All lines post a sign that diapers aren't allowed however I've never seen anyone enforcing this rule.)
Make sure you read my articles on this site about cruising with babies and toddlers, along with my article on Alaska for families.
Let me know how it was upon your return!
Smooth sailing,
Luisa Frey Gaynor
Family Cruise Editor