We sent a postcard home :)
They do not sell postcards at the post office, but we were kindly directed to a stationery store nearby, unfortunately this store has a small selection of postcards, but it is inexpensive only 1.5 dirhams, the postage stamp cost 4 dirhams.
Friendly staff. There are no postcards in the post office and they were not found in various shops within a radius of 1 km. There are stamps from 1 aed. See the opening hours.
Works only on weekdays, very nice operator. Unfortunately, postcards are not sold, I had to look in the shops of expensive hotels, but stamps are inexpensive.