The Phoenix and the Carpet - E. Nesbit

The Phoenix and the Carpet is a fantasy novel for children, written in 1904 by E. Nesbit. It is the second in a trilogy of novels that began with Five Children and It (1902), and follows the adventures of the same five protagonists – Cyril, Anthea, Robert, Jane and the Lamb. Their mother buys the children a new carpet to replace the one from the nursery that was destroyed in an unfortunate fire accident. Through a series of exciting events, the children find an egg in the carpet which cracks into a talking Phoenix. The Phoenix explains that the carpet is a magical one that will grant them three wishes per day. (Summary from Wikipedia)