Some tips and advice on taking Dragonlance material and adapting it to Quelmar:
Existing Elements
The Cataclysm
Quelmar has a number of Cataclysm but so far no one has defined an ancient one like the one that defines the Dragonlance setting. However, the end of the Holy War and the lead in to the Realm War I are similar world-rebuilding eras that mirror the Cataclysm. Perhaps a meteor was thrown onto Quelmar too as part of the final chapter of the Holy War?
Perhaps look at inventing Quelmar's own equivalent of the Cataclysm, or use something like The Curse of Life, The Arctic Autumn, The Razing of Isonhound, the The Umbral Flood, or another wide-spread source of disaster.
Knights of Solamnia
You can use the Knights of Wold.
High Sorcerers
You can use the Wold Order
Takhisis
You can use Tiamat
Three Moons
You can use Selune, Correlon, and Eros (the domains of Light, Fey, and Crystal) as the three different "Moons", depsite the fact that in Quelmar they share one celestial body.
War of the Lance
You can use either The Holy War or The War of Many Names, though if you use the latter it's recommended to use only the early years, when the war was exclusively focused on Dragons.