The most common and most likely answer to this crossword clue is the 8 letter word FLIRTING
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More clues leading to the result FLIRTING
Buddy explains!

The straight part
We know that "One’s right, during dalliance, so to be doing" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case one’s right, during dalliance, so to be doing = flirting.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does FLIRTING mean?
FLIRTING verb- To throw (something) with a jerk or sudden movement; to fling.
- To jeer at; to mock.
- To dart about; to move with quick, jerky motions.
- To blurt out.
- To play at courtship; to talk with teasing affection, to insinuate sexual attraction in a playful (especially conversational) way.
- To experiment, or tentatively engage, with; to become involved in passing with.
- A flirtation.