Not a fan of putting mousetraps or poison out for the critters.
The bait and poisin ATTRACT the critters.
Your baby will be safe as long as there's no food source nearby and you take the precautions with steel wool, mothballs, and/or dryer sheets.
Critters want 3 things... shelter, food, and water. Take away their close proximity to each other and viola... NO CRITTERS.