I'm a big fan of google docs, but I havne't tried it for layouts like this. I've had good luck with OpenOffice though.
I would design something like this in Google Drawings (available in Google Docs) or Inkscape, but feel free to keep using your existing design software if it has a usable export to SVG or PNG.
Export the design
You want to export the file from your design software into something you can load into the word processing software you choose to use. Exporting as an SVG will give you a vector file that should print at the maximum resolution of your printer. You could also export an PNG, but that will give you a bitmap that may be higher or lower resolution than the printer. If the PNG gets rescaled at a factor that isn't a multiple of 2 you can end up with artifacts. PNG files are also much bigger than an equivalent vector file. Disk space is cheap, but larger files will be harder for many printers to receive and process.
Paper or Cardstock
If you really need this exact size of output I would layout a page with crop marks around each image and then use a paper cutter to trim them down to size. I'd use a 28# paper or cardstock so they feel substantial.
It is interesting to me that your size is very close to US business cards size (3.5" x 2.0"). If you can live with that size you can easily get prescored sheets from Avery or their many competitors. This will let you skip the paper cutter and also means that there are pre-defined layouts for these from Avery and preloaded in OpenOffice and presumably MS-Word as well.