The phrase "go to dogs" means to deteriorate or become ruined. While there are many words and phrases that could be considered synonyms for this phrase, there are few true antonyms.
One possible antonym could be "thrive" or "succeed." If something is thriving, it is growing and prospering, which is the opposite of deteriorating. Similarly, if something is successful, it is doing well and achieving its goals, which is the opposite of failing.
Another possible antonym is "improve" or "restore." If something is improved or restored, it is being made better or returned to its former state, which is the opposite of becoming worse or deteriorating.