What is the name of a looney toons cartoon where an Indian trying to hunt moose?

There isn't a Looney Tunes cartoon with an Indian character hunting moose. The Looney Tunes cartoons often featured caricatures of different ethnicities, but they usually avoided depicting Native American characters in a way that could be considered disrespectful or offensive.

It's possible you're thinking of a different cartoon or that you've misremembered details. Do you remember any other specific details about the cartoon? This could help narrow down what you're thinking of.