Help finding a sci-fi movie title
From what I can recall, the movie I'm looking for strikes me as being from the early 60s. This is all foggy, but I remember a boy being given a rock by his father, which he would keep under his pillow, and it would cause him to dream of a world with two moons (or possibly suns). He grows up, and, through a forgotten sequence of events, actually goes to this world. There are these circular teleportation platforms that when stepped upon, transport you (in a puff of smoke) instantaneously. I believe this is how they escape back to Earth. Something about how an older scientist who drags his female assistant around as they flee from danger reminds me of the Quatermass movies, but I've recently seen all of those (I think), so it's not one of them. When I was a kid, this movie would often come on at a million-o'clock in the morning. Can anyone help?