Mostly I find the one year olds that are just mastering walking spend a lot of time just walking and considering the size of their legs and their stride - once around the kitchen is a lot further than it looks.
There are a lot of poems you can act out that have actions - especially things that have you "reaching high to touch the sky" or "crouching down to touch the ground".
I also have a shelf that runs the length of the playroom and toys are on it so the kids stand at the shelf to play and that is a way of exercising too as compared to sitting on the floor to play.
Watch as the little ones play and you will be amazed at how much they are actually moving. When they play blocks and build a tower, they reach down and pick up another block and then reach up to put it on the stack.