Hi Corrina,
"Stroller" is the only term I've ever heard in the U.S. to cover anything which a baby or toddler rests in and which an adult pushes. Maybe "pusher" is used in other parts of the U.S.?
At the risk of sounding presidential with my next phrase: My fellow Americans, what term(s) do you use?
Joy,
Lynn
p.s., Out of curiosity, I searched for "pram" on the babiesrus.com and amazon.com web sites. It appears that toy strollers designed to push dolls in are sometimes labelled as "prams," and such toys are both of the bassinet (or car seat)-carrying style and the style designed for older (toddler-age) children. The real thing, however, is always called a "stroller." (On amazon.com, however, there were some items labelled as "pram strollers." I guess they were covering their bases.)
The search for "pusher" on the two sites didn't return anything relevant.
