Is a last minute trip feasible with accommodations?

I found great airfare through the rest of summer to Iceland and am tempted to jump on it for mid August or so. I pretty much know the itinerary we’d do (a fairly typical 9 day Ring road with snaefellsnes detour). But my question is would the accommodation situation be a problem this close out? I’ve never really looked into the accommodation aspect of the trip before. We’d need rooms with 2 beds, and it sounds to me like there aren’t a lot of options in a lot of the places you need to stay for the route? If anyone knows any tips or suggestions for reasonable stays, appreciated. Or if it’s just not feasible to find places a month out that wouldn’t be outrageous