Wow, you're growing a close bond with your dragon! I think [Your Dragon's Name] is ready to grow older. Go to the Hatchery and stand in front of the Dragon Hearth. That's the pool of lava! Your dragon will use that heat to shed skin and grow.
You'll be able to customize your dragon a little bit more. It's so exciting! You can go there whenever any of your dragons reach Rank 5.