Well, Dubai is relatively inexpensive for taxis.
Taxis are equipped with a meter so it depends on the destination.
At 1 am, considering a trip to Dubai Marina (a relatively far destination), you may spend around the equivalent of 30 euros.
That is one way trip for two person with two pieces of luggage.
Traffic shouldn’t be heavy at that time (although it depends if it’s a festivity or a normal mid week working day) and you may estimate some 40 minutes to destination.
With traffic, that jumps up to 90 minutes.