The phrase "going dogs" has a few synonyms that can be used as well. If you are trying to describe going after something with great intensity, you might use the phrase "hot on the trail." If you want to describe someone who is persistently pursuing a goal, you could say they are "driven." Alternatively, if you're trying to describe someone who is travelling quickly or hastily, you might use the phrase "racing." Finally, if you are trying to describe a group of people working together to accomplish a task, you could say they are "collaborating." There are many different phrases and words that can be used to replace "going dogs" depending on the context and what you are trying to convey.