You will not have a problem as there is at least one vegetarian entree choice every night as well as appetizers and soups. It is the Vegans who would have problems.
Explorer of the Seas October 2013
Caribbean Princess July 2006, May 2010 & November 2012
Monarch of the Seas November 2008
Crown Princess November 2007
Celebrity Zenith November 2005
Enchantment of the Seas August 2004