With other pets
Actually, adding another dog in your household will not be a problem to well trained red heelers. If your red heeler has been well-socialized then more likely you will not be having problems and the new puppy will be accepted pretty quickly. If you will be adding an adult dog in your household, acceptance is a little bit difficult but not impossible.
The first thing that you remember to avoid fights is introducing them in a place other than your house. This will avoid territorial issue with your Red Heeler. Remember that Red Heeler is very protective when it comes to his master’s properties. Bring home with you some blanket of the new dog to help your Red Heeler familiarize the smell easily. It will give him the idea that the smell is allowed inside your house. Once your Red Heeler gets used to it, you can take the puppy or the dog home.
For the first few weeks, put them in a separate area where they see each other but avoid them to have direct interaction. Placing them in a separate room with a glass door is a good idea. Feeding them close to the glass door is a good way to see things. Try to observe their reaction towards the other while eating. It is always better to be on the safe side. Remember that Red Heeler is a dominant breed so you should watch for it from time to time. Take time and let them adjust with each other.
Jealousy can start the fight. Remember to give equal attention to your dogs. But consider giving it first to the top dog or the dominant one. This will assure him that he still has his position and prevent attacking the subordinate dog. Try to resist the cuteness of the puppy or else, you will be putting him in trouble. Be sure to have enough toys for them to play to prevent fighting over a toy.

