You should really ask the print shop about how to set up your file. They should be able to send you a template of the punch form used and give you some guidance.
That said, a PDF can only ever be rectangular.
My guess would be that the print shop needs a file where the irregular shape touches the sides of the rectangle. The bleed is added all around the irregular shape.
The yellow area is your design, the cyan stroke is the document bounds and the magenta stroke is where the final print is punched.
What Wolff said is correct. Also, brochures like this cost extra typically where I'm from, because of its unique form.
When you set up a print file, there should be three main lines:
- die line: where the paper will be cut giving you the final shape and size
- safe line (safe zone): usually .125 inches within the die line. Make sure your art does not surpass this line or it may be too close to the edge and risk getting cut off
- bleed line: usually .125 inches outside of the die line. Make sure art that you want going to the edges actually reaches the bleed line, not just the die line.
Lastly, make sure the printer does not print your lines!! Set your line layers to "Template" (double click layer for this option) or label the layer as "Do not print." You can also state to not print those lines. However, if the printer sends you the die line, they may have all these layers set up appropriately already.