The idea is solid, but the calculation is fundamentally wrong, because you're not separating the source of the IP for your formula. Starting pitchers and relievers are completely different beasts, so what you'd have to separate both IP and ER from starters, which is entirely possible by using the following Fangraphs link:
http://www.fangraphs.com/teams.aspx?pos=all&stats=sta&lg=all&type=0&season=2009&month=0
Export to Excel, and calculate from there.
Using this separation of starters and relievers, you come up with the following results:
2009 Starter's IP: 28,251
2009 Starter's ER: 13,977
First, ERA: 2009 Starter's ERA: 4.45
Now let's use your formula to determine how many runs could a pitcher give up from innings six to nice for a start to be considered a "Quality start".
28,251/6: 4,708.5
28,251/7: 4,305.8
28,251/8: 3531.3
28,251/9: 3139
6 IP: 13,977/4708.5: 2.96 (Round up to 3)
7 IP: 13,977/4305.8: 3.24 (Round down to 3)
8 IP: 13,977/3531.3: 3.95 (Round up to 4)
9 IP: 13,977/3139: 4.45 (Round down to 4)
It's essentially the same result as the typical quality start, but for pitching eight or nine innings, allowing four runs instead of three would still result in a quality start, all of this utilizing the League average as a benchmark. Even more interesting is the fact that the league average ERA is exactly the 4.45 mark that you would receive from an average pitcher's nine-inning start.