This will work very well. 2206 has an alcohol tolerance up to 9%, so you shouldn't have stressed it out too much, and, as you point out, you will have plenty of yeast. My only suggestion would be to pitch the doppelbock shortly after removing the porter off the yeast cake, so your yeast has maximum viability.
Brody's Brew House
Primary: American Pale Ale, Coffee Porter(
Seconary: Don't use one, generally
Planned: Either a brown ale or a Scottish Strong Ale
"For a quart of ale is a dish for a king." - Shakespeare