Story of the bunny: Bunny stars in the movie Con Air. Bunny is discarded as a prop and later bought by Dave. Dave sends it to John as a birthday present.
John eventually gets into the Medium and into the Land of Wind and Shade. Along the way the bunny flies out of his Sylladex into an oil river. The bunny is damaged and oil-stained. Then John goes to the Veil, where he makes the paradox clones and gives the oil-stained bunny to baby Rose.
Rose, later in her life, tries to repair the oil-stained bunny to give it as a birthday present to John, but doesn't finish in time. Before entering the Veil, John finds the unfinished knitted bunny and takes it with him. After making the paradox clones he gives the knitted bunny to baby Jade.
Jade probably repairs the bunny sometime in her life with robotic parts. Then all the kids work together to create the most awesome weapons ever. (Warhammer of Zillyhoo (hammer), Ahab's Crosshairs (rifle), Quills of Echidna (wands) and the Royal Deringer(broken sword)) The Hammer of Zillyhoo is probably made by John, as it's a very plausible theory that
this is, in fact, the hammer, because it is a (non-canon) hammer in Problem Sleuth.
The box containing the bunny and all the weapons was probably sent back in time from an alternate timeline (the mess-up the trolls talked about before) where Jack Noir did not kill the Black Queen because he did not have the bunny. Jade's pen-pal from the alternate timeline may very well be Jack Noir (or one of the other agents) or it could be a troll.
After being sent back in time the bunny is sent to John as a present. However it is left in the car by Dad after he acquires the mail. Eventually the car falls down onto the LOWAS and AR? finds the present. He brings it to Derse. PM? receives an etched tablet telling her to find the present. She asks Jack Noir for it and he sets her on a quest to bring him the 2 white crowns in return for the presents. After she leaves Jack uses the bunny to kill the Black Queen.
After a lot of stuff happens PM? has both crowns and kills HB so she can use his communicator to arrange a meeting. Jack Noir, now Sovereign Slayer, brings her the box. She then delivers it to John. He reads the letters. Among them is a list of contents naming the unknown weapons. Sovereign Slayer arrives to take John's ring but the bunny gets out of the box and defends him.
tl;dr: Weird time+plot stuff happens.