Around two years I give mine a travel size pillow. I make the pillow cases from existing ones I have, or buy a new set of regular size ones that they like or ones that match their room. it very easy to do. Just turn inside out, place the pillow on one side edge and the opening. measure out about two inches from the pillow, around the bottom and the edge that has the excess material. Just use a pencil and a ruler and draw your line. then straiten your seams and sew along your lines, one on the bottom and one on the side. cut the extra material off and turn it right side out. Done, now you have a Cute! travel size pillow case that can be just theirs. My girls have loved them. After they graduate from the toddler bed to a twin size then I upgrade their pillows to the regular size ones.
Have fun! When she enjoys pretending to lay on your pillows, then you will know that she would love her own. another good sign is when she wakes up in the same position that she went to sleep in, well at least the same side of the bed:)