The dog may kill them. I would just keep them in the pen. It looks like it is small enough to move around the yard.
We do plan to make them a bigger pen, as the 'tractor' is insanely heavy (re-used free wood, doesn't necessarily mean light, lol), and our property we realized is much bumpier/hillier than we realized, when we went to place it, pretty much nowhere worked.
But no worries, our chickies hang out in the run of their coop lots now! :)