Stardust is not species specific however it is a very valuable resource and should be used wisely.
You cannot purchase stardust and there are currently two ways you can collect it.
- Capturing a Pokemon will give you 100 stardust alongside 3 candy
- The defender bonus that can be earned by defending friendly gyms will give you 500 stardust alongside 10 Pokecoins for every Pokemon you have defending a gym. This bonus can be collected every 21 hours and you can have up to 10 Pokemon stationed in gyms at a time.