G`day. I know its a bit of a drive but you could try Stanley state forest near Beechworth / Yackandandah. Has good camp spots along the many creeks. Some people do have dogs but most camp spots are far enough apart not for them to bother you. If entering from Beechworth, there is a small lake called Fletchers Dam (off the Beechworth to Stanley road), good for a swim, canoe or fishing. All roads are fairly reasonable, easy access to most camping spots. If entering from Yackandandah, there are numerous camp sites along the creeks, but most are shallow (about knee deep) but still suitable for "swimming" in. Very popular spots during most public holiday periods.