I've never had a household that was devoid of canine and feline family members so that might affect my answer, but, there really isn't a timeline. Just as with a hereditary family member, they're not "replaceable" in the sense one might "replace" a significant other. If you picked up a new kitty a day after losing your long time feline companion, you're not somehow replacing your old family, you're rescuing new family that can help you work through the grief of losing someone special to you. Each pet we take into our homes is a unique personality that can't be erased once they are no longer with us, and it become apparent when you learn to interact with your newest adoptee. What matters is your capacity to open yourself up to loving this new family member: whether or not you are able to process grief with the help of others or if you have to shut down to do so. If the answer is that you can love someone while grieving for another, then you can adopt a new pet right now.