Craft ink is actually recommended for stamping on fabrics!
Once you heat set the ink, it should be permanent. Just to be sure it takes, though, you should launder (without using fabric softeners or dryer sheets) anything you plan to stamp to remove the sizing. It's nontoxic, and I would think it's gentle enough for touching delicate skin. I've seen several adorable examples of baby onesies that were stamped with craft ink -- my upline even had one as a sample a few years ago at one of her workshops!