From the Super Mario Wiki
Glowing Rabbits are rare, shiny types of rabbits that appear in Super Mario 64 DS. When 50 Power Stars are collected, Glowing Rabbits start to randomly appear around the castle in place of the character's other rabbits. There are eight Glowing Rabbits total. When all eight rabbits are caught, the player is rewarded with a key that unlocks the last door in the character selection room, which contains a secret Power Star. Glowing Rabbits no longer appear after finding all of them.
The final Glowing Rabbit caught states that it is the eldest of the Glowing Rabbits. Additionally, each rabbit before then states that it is the "second fastest of my eight brothers."