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Although you are able to Transit Without Visa (TWOV) through Dubai, as a Serbian passport holder, you must obtain a visa to leave the airport during the layover. You can use the Emirates tool to check your visa requirements. It does indicates that you need apply in advance for a visa, should you decide to leave the airport.
If you are travelling to or stopping in UAE with Emirates or Etihad, you can apply for your UAE visa through the websiteβs Manage a booking tool after booking your flight.
Otherwise, you would have to apply for a visa at the Embassy of the United Arab Emirates in Belgrade.
Burj Khalifa and the Dubai Mall are about 15 km from the airport, 15-20 minutes by taxi.
As for safety, Dubai and the UAE rate very highly in this regard, by both residents and tourists, men and women.