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No you do not. But I hope you have made arrangements for any hold luggage. The requirement for visas while in transit applies to a lot of travellers but at not very many locations (so far!).
Courtesy of KLM:
TWOV (Transit Without Visa):
Visa required, except for Holders of confirmed onward tickets for a max. transit time of 24 hours.
Visa is required for transit between Dubai International Airport (DXB) and Dubai Al Maktoum International (DWC).