When exporting to an image, you can choose the resolution, for example 300 dpi (dots per inch). Just make sure to use the same setting on your printer.
It might be useful to add a small calibration scale at the edge of your layout, e.g. small dashes of "dimension" or "silkscreen" spread 0.1" apart. You can then check with a ruler that the scale is OK.
You can also avoid inverting the image outside of Eagle, by choosing an appropriate color theme in the preferences. A white background is not comfortable for editing a PCB layout, but useful for export.