Your Dragon pickaxe can only be gilded if you already have all 5 pieces of the Golden mining outfit obtained in the Lava Flow Mine. Which requires completion of King of the Dwarves, Forgiveness of a Chaos Dwarf, and My Arm's Big Adventure to access.
Note that this pickaxe cannot be upgraded to a Crystal pickaxe. You will need to ungild it by speaking to Foreman Jack first.
Can be upgraded to an Imcando pickaxe by Thurgo if all requirements are met.