My son and I have stayed there, so I texted him to ask since he's in the Navy. He's stationed in Okinawa now, but he said he doesn't know if they accept small dogs, to give them a call.
They usually have a pet policy. Call the lodge to see if one of those rooms is available. This only goes to people who comment on the lodge, not people who work there.
Thanks! Your answer is awaiting moderation.