There is no "DPI" setting in FW as it is a screen graphics program. Your steps otherwise are correct though. Just bump up the Pixels/inch (PPI) value to 300. Assuming there are no bitmaps in the design, it should scale upwards fine.
Keep in mind too that FW has no concept of color profiles or CMYK, so printing the image may take some testing.
Thank you. Would Photoshop be the better application then?
For printing? Photoshop, Illustrator or InDesign.
You may be able to export your FW design to Illustrator by choosing File > Export >FXG and Images. If it's all vector, it should come over fairly well.
If there are bitmaps though, you'll need to pull in the original artwork again to work at the higher resolution.