I have done a couple of those (pic in my photos)... I used a cookie cutter and modified the wheels a little, but used gumpaste.. It is actually quite easy.. Attach a skewer in the back to stick in the cake..
I agree that you should use gumpaste or a fondant gumpaste mixture for the stroller. The flowers inside the wheels are are made with a tiny wilton fondant cutter that has several shapes and a little purple plunger. The very center or hub of the wheels appears to be a pearl. I would just roll it out and freehand the design of the basic body of the stroller and then make a little roll for the handle.