I would say the second option - "She skipped off, singing"
It gives a visual of her being very happy, instead of just saying she was happy.
Answer:
She skipped off, singing.
Explanation:
The second option shows rather than tells, because it has more emotive words and it also creates a sensorial experience with the use of the word "singing" it makes the reader imagine the person repeating a tune, and this also makes the mood merrier, then the action of skipping off instead of walking also evokes the figure of a happy child.
