The common US term for "perambulator" (pram) is a "baby carriage" or "buggy."

A baby carriage is a cart which is designed for moving a baby around while the baby is in a lying position, also known as a stroller or a pram.

Pram (if the baby lies down) or Pushchair (if the baby sits up).

The sit-up type / recliner is VERY commonly refered to as a 'buggy' too ... as in 'baby buggy'!

A nanny's carriage is a pram. (pram=a conveyance for baby transport ["perambulator" in full)

stroller, pram ( shortened from parambulator ) A baby buggy and a push chair.