You are a little late for planning your vacation during eid.... But there is hope if you get lucky...

Try online booking for your tickets, www.qatarairways.com or www.emirates.com, as a last option you can try different travel agents they usually end up having reserves. But booking online is the quick way out, its worked for me many times at the last minute. For Hotels there are plenty of sites you can do it through just google Dubai hotels, you might get lucky at one of the many listed...

My all time favorite is www.expedia.com for Hotel and airlines combined, . THree days is enough for a first timer and is better since you would not have budgeted...You can plan for another trip after you become a little familiar with the place... One thing I know is that Dubai makes you want to blow money, especially first timers so be careful and keep an eye on your credit cards you tend to swipe away...