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: Scottish Strong Ale
Seconary: Don't use one, generally
Kegged: Sweet Potato Saison
In the fridge: Czechvar, New Belgium sampler
Planned: Either a Porter or an AIPA. Possibly a RIS.
"For a quart of ale is a dish for a king." - Shakespeare