We might cross paths. I'll be with a group of about eight, paddling from Corowa to Echuca, starting just before the last weekend of October. The trip leader is experienced in this, so I guess there's a bit of knowledge in his choice of season. There's lots of trip reports on the web. Search for keywords "murray river kayak".
A couple of guides which are regularly used by river travellers are the Murray River Charts by Maureen & Barry Wright (http://rivermurraycharts.com.au/
), and the Murray River Access Guides (http://www.chartandmapshop.com.au/28060 ... s-Bundle/0
If you intend to include the upper Murray from around Bringenbrong to Jingellic, beware. If the level is too low you'll keep scraping on gravel races, and if too high you'll need to know how to handle your kayak or canoe in medium swift moving water. Get advice about which gauges to check and what levels are suitable. Further upstream than Bringenbrong is reputed to be serious white water.
After writing the above, just noticed you're in USA and don't own a kayak. A solo multiday river trip for an inexperienced paddler without suitable camping, foods, clothing and safety equipment isn't a safe way to go. That's a warning just in case it's relevant.