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The description seems to use the terms 'earthly domain', 'celestion domain' and 'board' inconsistently. When you say 'bring a Watcher onto the board', you seem to mean 'into the earthly domain'. The board is 11x11, and the Watchers are already on it.

Any empty square in the "celestial domain" becomes available for the game.

What does this mean? Does it become part of the earthly domain, so that Watchers can now be moved to it and flipped there? Or does it mean that ordinary pieces can enter the celestial domain, but through non-captures only?

Peacemaker moves as Duck in Duckchess.

One additional move by either moving a Peacemaker one square in any direction, ...

This is not how a Duck moves in Duck Chess...

Watchers cannot be moved into the game if there is no empty square next to them.

This is not a new rule, but a (rather obvious) consequence of the fact that the Watchers move like a Queen. Better omit it.

Watchers could be represented by neutral checkers pieces, allowing them to be flipped over in order to reveal their power. 

This is not a rule, but a suggestion how one could play the game over the board using 'woodware'. Such suggestions belong in the 'Notes' section of the article.

When placing a Watcher into the board, a player has to make sure that his own King will not be in check if it turns out to be an enemy piece.  

A player cannot place a Watcher next to his own King.

The second line seems to follow from the first, but not entirely. Can the Watcher be placed a Knight's jump away from your own King if you are sure that it cannot be a Knight, because all enemy pieces with Knight moves already have been flipped?

Treasurers can never be removed from the board. When captured, they will switch sides as many times as it takes. A Treasurer cannot be captured twice in a row.

What does this mean? Does the capturer survive, and if so, where will it end up. Where will the collor-flipped Treasurer end up? If it is an adjacent empty square, what happens when there is no such square (which could happen when it is captured through a Knight jump)?

I might need some help with drawing the diagram and I would really appreciate it if someone could help me with this. 

How about just writing a FEN for the position between [fen ] and [/fen ] tags? That shouldn't be so hard. You would just have to pick suitable images for the unorthodox pieces from the Alfaerie piece set, and put their ID in the FEN. Or, if they do not have a single-letter ID, write their full name between braces {} in the FEN.