Not 100% sure how the government of the new Dwarf capital will run, But I had a few ideas I thought I would run by everyone.
King
Figurehead of the dwarves. Who everyone looks to for strength and power.
High Council
Handful of members that each rule a sector of the Dwarven kingdom. Guilds, Economics, War, Clans, and Diplomatic.
Weekly meetings of each of these sectors allows the heads of each are to relate questions, problems, and suggestions to the High Council members. (ex: Head of each guild meets with Guild Council member every other Tuesday)
Bi-Weekly Council meetings allow high council members to relay these findings to the king and decisions can be made for the betterment of the kingdom. In decision making, King counts as 2 votes, meaning 3/5 High council members could overthrow his decision.
Monthly elections within the sectors would allow members who are interested in gaining experience in a government position the chance to sit on the council. (Fresh ideas every month or so.) Slumping progress or bad showing by a Council member could enact an emergency election within the sector.
Clan meetings, guild meetings, Legion meetings, and economic summits could happen on a regular basis and allow hard working members to rise up and voice there opinions, and possibly put new leaders at the head of some flailing groups. Likewise, Diplomacy with other nations could benefit from monthly feasts, tournaments, or gatherings of any kind.
Just some thoughts. Figured I'd throw it out there.