Each of us has to deal with the death of a little one in their own way and own time ... there is nothing set in stone to cover this.
If you want to get a chin soon, I would first clean the cage thoroughly (not because of what might have been in your home, but what your little one brought into your home from somewhere else). Dispose of all food and anything that can not be sterilized.
If you have any other pets, do not allow them in the Chin's room, especially if they are allowed both inside and outside of the house. Keep a bottle of instant sanitizer near the cage and insist those handling the chin clean their hands first.
I strongly suggest getting a chin (preferably 2 at the same time), from a reputable breeder rather than a pet store. Chinchillas in pet stores are usually mishandled more than they are handled properly. Chinchillas are very fragile in many ways.
Nothing will ever take the place of your first one, or any number of them in between, each chinchilla has a way of making it's own special place in your heart that no one or no thing can ever fill it's place there.
Sometimes you just have to visit a breeder and their chins a few times ... when you see one you just can't leave without, then it is time to bring a new little one or two home with you.
Hope this helps a little.
Big Chinnie Hug!
Jo Ann