To start with, in case you're unaware: At 3 years old, your dragon is a wyrmling. Dragon age categories are provided in a table on page 86 of the Monster Manual.
Next, there's the question of which dragons have lair actions and regional effects. The sections describing each dragon type's lair actions and regional effects aren't attached to particular dragon sizes of each type, so it's possible that all dragons can have them. However, I believe the answer is actually adult or ancient dragons only, or 101+ year-old dragons.
Why do I think that? Well, on page 11 of the Monster Manual, it describes Legendary Creatures. It talks about their Legendary Actions, their Lair Actions, and their Regional Effects. The whole section is relevant here, so I won't bother quoting it, but the important bit is that:
Legendary creatures can take special actions outside of their turns
A legendary creature can take a certain number of special actions - called legendary actions - outside its turn.
I'm sure you can see where I'm going with this - only adult and ancient dragons have legendary actions, which leads me to believe that only adult and ancient dragons are legendary creatures, and therefore they're the ones with Lair Actions and Regional Effects. This is backed up by the fact that only adult and ancient dragons have Legendary Resistance. Also, the sections describing the Regional Effects of dragons all seem to use the following wording:
The region containing a legendary [colour] dragon is warped by the dragon's magic [...]
So, all in all, I'm inclined to believe that dragons are able to use their lair actions and regional effects once they're 101 years old.