You have a couple of options:
1. Have your printer deal with it. It probably won't cost you more than 1/2 hour's art time... as long as the source artwork is good. For a single piece this is your best bet.
2. Farm out the conversion. There are a number of people who specialize in converting raster artwork to vector. I've used the
vector doctor a few times.
3. Pick up Illustrator CS2 and learn to use the livetrace feature. Since you're already experienced with a drawing package, you probably won't have a hard time doing it. This is a worthwhile long-term investment.
From the artwork on your site, it doesn't look like vectorizing your existing artwork is a realistic option. That doesn't necessaritly limit you to inkjet or
DTG... look into the process color option.