A 13" x 18" low-loft pillow is the recommended size for toddlers 2 - 3 years. Although that may look small from an adult's point of view, or on a toddler bed, remember the important factor is the comfort and support of your precious child; not the decor. If you want pillows to fit the bed or the bedding that came with your sheet set, by all means use what you will but remember to remove them during the night and give your child the appropriate size pillow for sleeping.
In addition to the orthopedic reason behind a small low-profile pillow, the smaller dimension often encourages a restless child to move less during the night. Many parents are surprised, but pleased, at finding that their toddlers are more stationary as they learn to stay on the pillow while sleeping. Please remember though as every child is different they will adjust at different rates to a new pillow. A Little Pillow Company's Toddler Pillow is the appropriate size and loft for 2 - 3 year old children.
Now as there is a definite growth difference between a 24 month old and a 36 month old (the ages most suitable for our Toddler Pillow), we have an Adjustable Loft Pillow which allows you to customize the support as your child's neck grows. You simply take out some fill to make it lower for the younger toddler and add more back for the older.