Yes, "We have to be quick" and "We have to hurry" have similar meanings, but there's a slight difference in nuance:
"We have to be quick" focuses on the speed of an action. It suggests that whatever you are doing needs to be done fast.
Example: We have to be quick if we want to grab coffee before the meeting.
"We have to hurry" emphasizes urgency and the need to move faster to avoid being late.
Example: We have to hurry, or we’ll miss the train!
In many situations, they can be used interchangeably, but "hurry" often implies a stronger sense of urgency.