Check out Amy Karol's bend-the-rules Sewing for an easy, cute pattern for baby bibs. I got on a bit of a kick and made a bunch last week. They are a great way to use fat quarters. They'd be fabulous baby shower gifts too - so vibrant and fun.
I fiddled with the pattern later though, and enlarged it to fit toddlers. I found baby bibs pretty useless once my little guy was about a year old - just when he was the messiest eater. You need more coverage, you know? I couldn't find any larger bibs in stores.
I've got a set of three toddler bibs in cute, coordinating fabric in my etsy shop if you need a great gift for the toddler, really for the toddler's mom, in your life.