Other words for "jumping in excitement"

Solution 1:

You could consider using “hopped about/around” in a suitable simile to try to capture the image you’re after:

He hopped about/around like a [an excited] baby bunny/chick/sparrow, wanting to go as soon as possible.

(example usage from ‘Jeeves and the Christmas Grotto’ [Chapter 1, paragraph 5] via ‘archiveofourown[dot]org’)

Solution 2:

A few synonyms pop up if you google excitement - exhilaration, elation, animation, enthusiasm, eagerness, anticipation, feverishness, fever, delirium, agitation, emotion, fire, fieriness, intensity, zeal, zest; informal pep, vim, zing, spark

You could also replace jumping with bouncing which seems better to convey the idea of excitement.

He was bouncing up and down with enthusiasm. How about that?

Solution 3:

What WS2 said. I would like to add this:

Jump for joy, from TFD

to be very happy about something good that has happened

"Tina jumped for joy when she found out she'd be in the team."

Leap at the opportunity, from TFD (leap/jump at the chance/opportunity)

Fig. to accept an opportunity eagerly.

"Frank leapt at the opportunity to become a commercial artist."
"It was a great idea and we leapt at the opportunity."
"I would leap at the chance to go to Moscow."
"His company proposed to send him to England, and John jumped at the chance."