Your starter will certainly be viable a week later. They're hearty creatures, as evident by brewers being able to use yeast that is 45 million years old.
Yes, put it into the fridge and take it out on brew day. Pour off the liquid (although you don't have to) on the top and give the yeast a few hours to come up to room temperature. Then pitch as usual. You'll be fine without adding any extra wort.