Once you've unlocked the dragon, return to the central island.
Jump up the platforms behind the portal to the ice world until you're on the raised piece of land. Clean the area, and use the machine on the top. This will create a pipe that lets you walk safely between the upper and lower levels.FYI: after creating the pipe, move to the upper level; press and to summon your dragon; and you can grab a nearby egg by jumping and gliding.
FYI 2: it is possible to miss this. If you do, just return to the central island with the dragon; jump up those platforms again to the top portal; and put your tax tokens in the machine to create the pipe.