You need to create an outline, probably in Illustrator to make an outline that the forme/die cutter company uses. Speak to the company doing the printing. It may be the printer or s/he may subcontract this work out.
The alternative is to print on standard cut labels.
Thank you for the prompt reply Derek! I really appreciate it!
Here's a method for creating a contour line in ID that might work in many situations to create the die line you'll need:
Place the art, then copy and "paste in place" so you have two stacked images.
For this type of art it's pretty likely that there is a strong edge contrast, even a transparent background, so there's a good chance you can make a decent clipping path. Select the top copy, go to Object > Clipping Path > Options... and set it to detect edges (turn on the preview). Play with the tolerance and threshold sliders (lower numbers are likely to work better) until you get a path that matches the shape to your satisfaction, and set an Inset Frame value if you want to chop off part of the art (not likely) or enter a negative value for moving the line away from the art (very likely). When you're happy, click OK.
Object > Clipping Path > Convert Clipping Path to Frame, then double click on the art inside the newly shaped frame to select the content (or use the direct select tool) and delete it, leaving the frame and the other art behind it intact. Apply a stroke to the contoured frame, colored with a spot color assigned to die lines (die lines are always a spot color so they are on their own plate all alone), and set the stroke to overprint.
Group with the art and you're done.
Thank you Peter! My little brain needs specificity! Thank you for being so detailed in your response! Very helpful!!!