There are four main factors you want to consider when purchasing a pillow for a child: its size, its support, its ability to be cleaned, and the reputation of the company from whom you are buying. The first two are a necessity; the third and fourth highly recommended.
Regarding size: Please follow the pediatrician recommendation for a SMALL pillow, one designed to fit their little necks and bodies. Large, adult size pillows are just not healthy for little people.
Regarding support: Similar to the above, you absolutely do not want to give your child a pillow that is too high. This can strain their necks, cause discomfort and interfere with a proper, deep night's sleep.
Regarding laundering: Ironically, not all children's pillows out there can be washed and dried well so be sure to double and triple check the details. Children get sick in the night and sweat and drool far more than adults and therefore will need a pillow that can be regularly laundered. Pillowcases certainly help mitigate the normal wear of a pillow but this won't stop the extreme moments that every child has at some point during their early years. And be careful about the pillows that claim to be resistant to these moments (this includes dust mite covers) as they most often are made from a plastic cover which is extremely hot for a child to sleep on, not to mention not that comfortable. For those worried about the 'dust mite allergy', any pillow that can be regularly machine washed and dried will take care of that.
Lastly, be sure to choose a pillow from a reputable company. There has been a flurry of popup companies in the past few years cranking out children's pillows because they believe it's a quick way to make a buck without any real thought or care for longevity and quality. We have seen many of these copycat companies' products and have been appalled at the low workmanship and lack of real understanding about what makes a good quality, enduring pillow.