The phrase "on our quest" is correct and can be used in written English.
You could use it in any context where someone is in the process of actively searching for something or trying to accomplish something. For example: "We remained determined as we continued on our quest to find the missing painting."
Coral Morphologic believes that unlocking the secrets of coral sex is one of the most important scientific achievements we must pass on our quest towards preserving a sustainable future for our biosphere and all its inhabitants.
It means we made it out of our group and are continuing on our quest.
On our quest to find the best barbecue in Tennessee, we discovered Puckett's.
It was the second false wall my friend and I had passed through that day on our quest to buy knock-off designer bags for the magazine's Fashion Week-inspired Nine of a Kind, in this Sunday's issue.
Pursuing these directions should get us going on our quest, which I expect will last well into the twenty-first century, to harness the new technologies of information for the fulfillment of ancient human purposes.
For its part, "Major League Soccer continues to work with the City of New York and local elected officials on our quest to build a soccer stadium in Queens and are making progress with the project," said Dan Courtemanche, a spokesman for the league.
We begin to learn how our Warlock partners will behave and the characteristics of the various monsters we encounter on our quests.
With each year, we can count on continuing our quest for the pursuit of happiness and fulfillment.
Just as we had begun to move on from our quest to work Gary's tablet, the same kid who helped us earlier stopped at the table.
The story is both a metaphor for the blind faith of theatre itself and a beguiling meditation on our own quest for spiritual magic.
"High-quality content and innovative tech platforms will drive Vice through this next period of growth on our relentless quest for total media domination".
