Hi Ellie, and welcome to Cruise Chat.
You'll have a wonderful time on Infinity. There will be two "formal" nights where cocktail attire is perfect. Leave the long ball gowns home. On the other nights, a nice dress, pants outfit or skirt will work. Think of it as "going out to a restaurant" type clothing.
For Alaska itself, take clothing you can layer, with a warm, water repellent outermost layer. And take a hat and gloves. You'll want to be out on deck while cruising, observing the gorgeous scenery, and it can be cold, especially when cruising near a glacier. Take binoculars if you have space for them.
Infinity is a wonderful ship with great food and service. Concierge Class will get you fresh flowers and fresh fruit in your room, as well as other nice touches and amenities.