Soft pine is good for this, especially for Cockatoos. Please keep your babies wings clipped. You may be tempted to let their wings grow out, because it's nice to let them fly, but the possibility of them getting startled and flying off happens often and the chances of recovering the bird are slim. Toys with an extra long chain can wrap around the baby's neck. Mini blind cords are also a danger.
Babies can drown.
Avocados, chocolate and mushrooms are poisonous for them to ingest.