I'm moving house this weekend. How shall we transfer the dots?

If you still have the original backing paper, just put the dots down with the sticky side to the paper's glossy side. Alternatively, you can use baking paper, glossy magazine cover pages or the plastic pages of a clearfile folder.

For any larger decals, an idea might be be to stick the dots onto the fridge, or washing machine.  Something with a large surface, but that isn't going to get banged during the shift.