Cuardaigh means both "search" and "search for." So this sentence could mean both "we search our yellow bag (for something)" and "we search for our yellow bag."
If you want to include both objects in the sentence e.g. "We search our yellow bag for the lighter" it could be phrased as either Cuardaímid ár mála buí don lastóir or Cuardaimid an lastóir inár mála buí. I prefer the first of the two, as Dineen has ag cuardach dó meaning "searching for it" but it seems the 2nd type is more common on focloir.ie
Duo did not accept "look for" (as in "we look for our yellow bag). But Fócloir.ie suggests that "cuardaigh" can be translated as "look for" (https://www.focloir.ie/en/dictionary/ei/look+for and "did he have a good look for it? ar chuardaigh sé go maith é" https://www.focloir.ie/en/dictionary/ei/look#look__1). Is there a nuance I'm missing?