You have options for labeling, you can order fabric tags from someone and write in the date with a permanant fabric pen with a micro point and sew into a seam.
You can order a stamp and stamp it on the product, depending on the product this may not be asthetically the best option, and you would have to be be sure the ink in the stamp pad was permanant and safe.
Some people are producing their own on their printers using inkjet computer fabric you can buy at a joanns. If your item is too small for a sewn in label, you are okay with using a stamp or a sticker with the required info and attaching it to the packaging. This works for jewelry, hairbows, booties, stuff like that.
If you are making fabric items, you need to be also concerned with the FTC labeling that has to do with washing, fabric/fiber content and where the country the fibers came from. The FTC regs are older, and should have already been on fabric products.
So far it has been left to us to do what we need to do to comply based on whatever product we make. So whatever works for you, and you may need to use a combination of label types to get the job done.