For my 3 yo, what signs we should be looking for that she needs a pillow? What size of a pillow will be suitable for that age? She sleeps in a toddler bed converted from a cot and same size as the cot. Thanks!

Red Nose recommends withholding the use of a pillow (or other soft bedding) until the child has moved from the cot to a bed.
However, many children (& adults) do not use a pillow for sleep.
It is a very individual issue - even when children in a bed with a pillow, may not sleep on it.