What is the term for a small bed designed for newborns?

A bassinet, bassinette, or cradle is a bed specifically for babies from birth to about four months. Bassinets are generally designed to work with fixed legs or caster wheels, while cradles are generally designed to provide a rocking or gliding motion. Bassinets and cradles are distinguished from Moses baskets and carry cots, which are designed to be carried and sit directly on the floor or furniture. After four months, babies are often transferred to a crib. In the United States, however, the bedside sleeper is the prevalent option, since they are generally bigger, recommended up to 6 months, and often used up to a year.

Source: Wikipedia