How soon did you introduce pets to newborn

I want to buy a lifelike baby doll about a month before due date, one that cries etc. because both my small dog and cat startle easily and I think if they got used to noises like crying and me holding a baby before she is actually born might help them be calmer and act normal when I actualy come home with newborn for the first time and won't need to deal with added stress from pets reaction since they are somewhat use to the noises 

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