I travel fairly often for work, including through Dubai and I've never had any trouble. You can take your insulin and a needle or two on board. Make sure you have a letter from your doctor, sometimes security may want to see it, but I've never had to show it. In fact, the only time a security officer asked about it, he saw the pen, asked what it was I said insulin he said no problem and I was on my way.
As for being on the plane, I usually go to the toilet and inject after the meal. I don't do it before in case something happens and I don't get my meal in time or I misjudge to dosage because the meal was different to what I thought. You should always have some form of glucose available when on a plane in case of a low.