Is it important to establish a nap schedule?

Yes: Yes, but most children will establish it without too much help, as long as they are not bothered at random intervals. A schedule that works for one child may not work for another, even of the same age.

Yes: If you value your sanity, yes. Infants, toddlers, and parents of infants and toddlers typically do better with routines, schedules, and predictability. As the parent, you have some control over the schedule, and certainly know better than your child what they need. Use your authority to shape your child's routine to achieve their required hours while preserving your health and mind.

Night: But it is important to try to have a set time for bed time in evening and be firm with that as much as life allows. Try to wake them up same time every morning.