Unfortunately the fishing in Dubai isn't that good I'm afraid, particularly in the summer. I have done a lot of shore fishing over the years but I've only been once since the turn of the year because it has been very slow. You need a licence issued by the Municipality and the places you can fish off the shore are quite limited.
If you are keen on getting out there is a charter company in Dubai called Happy Days who mainly bottom fish but they take individual bookings and are reasonably priced. They will put you on fish such as sharry etc. Contact number is +971 50 818 6307.
There are other companies offering 'charters' from Dubai but most of them will be bottom fishing or trolling for 'cuda and the odd hammour. You'll be better off saving your money for a beer, it's only 8 to 10 quid a pint here
It may be worth you dropping into the Barracuda or Bluewaters Marine tackle shops located on Sheikh Zayed Road for some advice.
Soolyman Sportfishing operate out of Fujairah on the East coast and are a very good outfit. Unfortunately there was an incident involving the sabotage of four tankers anchored off there on Sunday so relations between the GCC / US and Iran are currently more fraught than normal