cockatiel laying eggs need some advice

we are a proud owner of a four years old female cockatiel named 'agatha'. we got her as a baby and hand fed her. her main diet is zupreme cockatiel pellet food and one serving of vegetables, fruits, bread, seeds, hay, cooked rice, and millets alternating every day. she gets her caged covered at night for about 10 hrs in summer and 14 hours in winter. she is completely feathered so she gets an hour flying time in the morning. she is very tame and sweet. she also gets an annual check-up from an avian vet.

this morning, we found an egg in the bottom of the cage, we assumed that she layed it on a ledge on the side of her cage and fell on the cage floor. we have cats so she does not like hanging out at the bottom of her cage. we left it where it is.

my question is, should we provide a nest for her so she can sit on her eggs? or just let her drop her eggs on the cage floor? we tried researching and there are a lot of opinions regarding this, some say provide a nest and some suggest to not give any to discourage her from laying more eggs. im just worried that if she kept on dropping her eggs on the cage floor and not having a chance to sit on it might trigger her hormones to lay more eggs. we also ordered some fake eggs for replacements.

we need some expert advice. thanks in advance.

eric