There are a few places in KV you can stay.
Glenmack Caravan Park is on the South side of town when you drive through. We have stayed here a number of times and enjoy the peace and layed back nature. I Believe they may still allow open fires on the camp site.http://www.glenmack.com.au/
KV Tourist Park is on the river beside the bridge. Has smaller camping sites then Glenmack but more facilities for the kids.http://www.kvtouristpark.com.au/
Bendeela Campground is about 8 kms from town. Dropped in for a day trip about two months ago. Space and lots and lots of it. Camping by the river. Lots of Wombats.
Only one toilet facilities is the big draw back, so bring your own.