As a veteran of many a Disney cruise, I will tell you that boarding begins as soon as the ship is cleaned and loaded from disembarking passengers. Although the official word is sometime around noon or 1:00, the ships often board earlier than that - usually around 11:30 in the morning.
My suggestion is to arrive early and receive the earliest possible boarding pass (used to be first come, first served in a long line, now it's done by number). The earlier you arrive, the smaller number you receive and the earlier you can board. An early boarding can get you an "extra" half day on the ship - all pools, food and amenities are available (although you usually cannot get into your cabin until after 2:00).
Last call for boarding is around 3:30.