Sounds like a nice tour, but as said you'll need at LEAST 10 days. I've done two trips 2,500 miles each both being 10 days. This included a stop over in Hungary for 4 days on my last trip. I want to do the ring and see my dad again, so this would be perfect for me. My dad lives on the south west coast of Lake Balaton where the beer is very cheap and great weather.
In terms of cost for fuel, in August the 100 octane was 1.72 euro a litre, so make sure you have plenty of cash. If you drive through Austria, Hungary, Switzerland and Slivenia you MUST pay to drive their motorways. I slipped up in Slivenia and had a 150euro fine!!!