The image gets scaled when it's printed. You can tell it to print any image the size you want, but if the resolution is low it will look very bad.
What determines the size of the print is the resolution (dots per inch) of the printer. It is possible to work it out from that, but it may be easier just to run a test.
Photoshop may contain some specific help on this.
With scaling disabled, or set to 1:1 -- If your scanner dpi matches your printer dpi, then it would scale 1:1. Scanning at twice the resolution would result in an image twice the size.
Since you state the printer is 300 dpi, then scanning at 600 dpi will give you a 2x image, but only if the print software doesn't do any scaling.