This was such a quick project! Start to finish during naptime, using fabric and clear contact paper, both of which I already had laying around (love when that happens). I got the idea here (very sweet Australian crafting blog). But I'm not fond of bias tape or binding (simply because I'm not any good with it yet!) so I just folded the edges over twice and used a decorative stitch in a contrasting color. I also didn't use a backing fabric because I just wanted to do a quick trial.
I did have trouble getting the contact paper to really fuse to the fabric, but I think I was just being too cautious with the iron and used a protective fabric that was too thick between the iron and laminate. My finished dimensions are too small for a real-life toddler, but little ones aren't too picky (heehee). Here are close-ups of the stitch and the wipe-down surface provided by the clear contact paper.
Once I perfect this, I think it would make a great personalized kid's birthday gift.