To apply for a boat dock permit in Alaska, you'll need to coordinate with multiple agencies depending on the location and specifics of your project. If your dock is in or near fish-bearing waters, a Fish Habitat Permit from the Alaska Department of Fish and Game (ADF&G) is required. The application involves providing detailed project descriptions, site maps, and diagrams, which must be submitted to the Division of Habitat.
https://www.adfg.alaska.gov/index.cfm?adfg=uselicense.docksramps_permits

If the dock is within a state park, such as those in the Matanuska-Susitna Valley, you must apply for a permit through Alaska State Parks, including submitting plans and paying a non-refundable application fee. Local government permitting requirements may also apply, so it’s important to contact your municipality for additional regulations. For a streamlined process, visit the ADF&G, DNR, and USACE websites for forms and further details on application requirements.
https://dnr.alaska.gov/parks/permit/matsudockpermits.htm 

For docks on state-owned submerged lands, a Land Use Permit from the Alaska Department of Natural Resources (DNR) may also be necessary. This requires submitting a detailed application to the appropriate DNR regional office. Additionally, if your project involves navigable waters or discharges into U.S. waters, you’ll need a permit from the U.S. Army Corps of Engineers (USACE) under Section 10 of the Rivers and Harbors Act and Section 404 of the Clean Water Act.