Right, the SSD1306 seems to have the DC-DC converter built into the driver IC, so you only have to provide a single supply voltage. It is a bit of a trap that the SSD1309 does not include the converter!
In your shoes, I would do the experiment with an external 9V or 12V supply for your SSD1309 display, as a learning experience -- but then switch to an SSD1306-based display for the final system you want to build. (If you can find one in a suitable form factor.) Adding your own DC-DC converter externally is probably more hassle than you need...