Where can you find stardust in Nintendogs plus cats?

Stardust is quite hard to get in nintendogs + cats

your dog will only bring you it when they are happy with you

you can use it at Mr.Recycle's shop to exchange it for rare items

once you have more trainer points he will begin to want stardust for things

that is your chance to exchange the stardust you found for the item you want he has on sale for it

It is very pretty and valuable.