Dawn's Quilava was obtained in DP143. After winning in the battle contest, Dawn received an egg as a prize. In the same episode the egg hatches, revealing a young and cute Cyndaquil. Even though it is still young, it wields powerful moves like Swift and Flame Wheel. Dawn chose this Pokémon to replace Ambipom (Since it is in training with the Ping-Pong Champion). Cyndaquil is pairing with Mamoswine in Dawn's latest contest where she is facing Ursula and her Plusle and Minun. Mamoswine and Cyndaquil are known for their fierce-ice combo.
Prior to Dawn leaving for Hoenn, Cyndaquil and Piplup work on a failed move. Cyndaquil wanted to come with Dawn to Hoenn and evolves into a Quilava helping her deal with a situation with some Ariados. In BW088, Ash is apparently pleased upon finding out it evolved.
Quilava is the eighth Pokémon to follow the pattern of premiering in a movie and then being captured by one of the main characters.
In all cases, the premiered Pokémon is not the same character as the one caught, just the same species. Dawn's Cyndaquil comes after Arceus and the Jewel of Life. This is only a technical premiere, as Cyndaquil was featured during the original Johto series as well.
Quilava is the only Pokémon belonging to a main character to have evolved in a side story episode so far, in SS024.
Dawn's Quilava is the last Pokémon to evolve with a white light surrounding them.