A row erupted last year as Peer, world No 22, was denied a visa following Israel's military offensive in Gaza in January 2009 and hence a was given a place in the line-up.
Tournament organisers said at the time that Peer's attendance would have "antagonised fans" and warned the "entire tournament could have been boycotted by protestors," posing a security risk to other players.
The Women's Tennis Association (WTA) fined Dubai a record $300,000.
Peer became the first Israeli to compete in a professional women's tennis event in a Gulf country after playing in the Qatar Open in Doha in 2008.
Meanwhile, American Venus Williams, the defending champion at the Barclays Dubai Tennis Championships, showed her love for Dubai on Sunday by celebrating the joint 10th anniversary of the Women's Open and the iconic Burj Al Arab hotel.
The World No 5, a five-time Wimbledon champion, was pictured alongside a giant '10' on the bridge leading to Burj Al Arab.