If you want to Stay at the Burj Al Arab you can spend that $1600 for on your hotel room for 1 night.

I'll suggest spending some more time researching, decide on a couple of candidate hotels and use their websites to check the rates.

Then the attractions you want to visit, most have websites with their costs.

You should define your budget.

To see the attractions I would opt to rent a car in Dubai (https://rentalcarsuae.com/) because it’s fast and cheap. Excellent Hospitality with not much burden to your Pocket.