More literal translations:
* Dans die hele nag: This translates to "dance the whole night."
* Dans tot die son opkom: This translates to "dance until the sun comes up."
More idiomatic expressions:
* Dans die nag deur: This is closer to the meaning of "dance the night away," implying dancing until late into the night.
* Maak die nag warm: This literally means "make the night hot," but implies a lively and energetic night of dancing.
The best translation depends on the specific context and the level of formality. For example, "dans die nag deur" would be a good choice for a casual setting, while "dans die hele nag" would be more appropriate for a formal event.