In an Australian cafe, office or casual goodbye, Have a good one often means “enjoy the time ahead”. One does not need to name a particular object. Context lets it stand for the day, evening, weekend or activity coming next, so there is no need to ask, “a good what?”
A: Thanks for the coffee. See you tomorrow.
B: No worries. Have a good one.
A: You too.
The tone is friendly and informal. The expression is not uniquely Australian and is also common in North America. In a formal email, Have a good day or Have a pleasant weekend states the period more clearly.
https://dictionary.cambridge.org/dictionary/english/have-a-good-one
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