Rabbits can carry a disease called pasturella which can be passed (airborne) to chinchillas and it is asbolutely deadly to them.
Chinchilla breeding is more than cute babies and money. It takes alot of time and money and alot of things can and will go wrong. You breed to better the chinchilla breed and not just throwing male and female together.
Maybe you should attend some chinchilla shows around your area. You can learn alot and what it takes to breed quality, healthy, chinchillas.
I have done much research on owning, breeding, and basic genetics for chinchillas and this is definitely not something you want to jump into.
They need to be in a environment with a stable temperature of 70 or lower. Chinchillas can overheat and suffer from a heatstroke in temperatures over 75.
SonnyWimps is right. Chinchillas cannot get wet unless ABSOLUTELY nessesary (meaning, their life depends on it!). Their fur is too dense that it can get locked in their coat if not properly dried and they can suffer from hypothermia.
In some cases when breeding, (especially for first time moms) with litters with 3 kits(baby chins)+ mom does not have enough milk in the first 2-3 days and the kits will fight over nipples and their fights CAN infact be deadly. You will have to rotate the kits every two hours so the smaller kits can have a chance at getting some milk.
Mom's can also die during the birthing process which will result in having to handfeed every single kit every 2 hours AROUND THE CLOCK with absolutely no breaks whatsoever. That goes on for 4-5 weeks until you can space the feedings more when they get their strength up.
Please, whatever you do, do some research on proper care of the chinchilla FIRST and make sure this is a pet you want to take on before you jump the gun on breeding these beautiful animals.
If you have any questions, feel free to contact me.