Despite the prevailing opinion that a cat and a dog cannot get along, this is not so. A dog and a cat are quite capable of peacefully coexisting side by side in the same territory. At the same time, the older and stronger will even protect the weak. You just need to correctly approach this problem.
First days
If one of the animals is an old-timer in the house, and a baby is taken to him, then this is a difficult case. The fact is that a baby can play too actively with an adult animal. It is clear that an adult animal may not like it. The kid will get "nuts", and this will once and for all establish the hierarchy in the house.
The kid should not be allowed to play too actively with an adult animal until the relationship is sorted out.
By the way, if you brought a puppy and a kitten to the house, then the process may not be delayed. Kids don't know that they are supposed to be at enmity.
In any case, when you introduce the animals, just let them go in the same room. Perhaps the friendship will be established immediately, if not, then you have to be patient.
Dating rules
You should not bring animals to each other on your own, this can cause them to conflict, which you will have to correct later. They can start a fight from the very beginning, during which you can get it.
It is best to keep them in different rooms, occasionally releasing the old-timer. Let them talk through the door for now.
As soon as the growls and hiss stop (if any), you can let them stay in the same room, but only with you. In this case, the old-timer should be launched into the beginner's territory, and not vice versa.
Be always on the lookout, a spray bottle with cold water will do the trick. If the animals start a fight, then it is best to "cool" them, and not to climb with your hands in order to keep these hands safe and sound.
Talk to an older animal, stroke it. Your older pet considers itself a full-fledged owner of the territory, and the arrival of a baby can be regarded by him as an occupation. Animals can be jealous too, so show that the arrival of the baby hasn't changed your attitude towards the old-timer in the least.
If the acquaintance went well, then again divide the animals into rooms. It is better not to let them meet in private for a while.
Never fondle a newbie in the presence of an old-timer, this can provoke a fit of jealousy. In the presence of a beginner, all attention is only to the elder.
You need to feed the animals from different bowls. Prevent one of them from eating from the other's bowl.
Gradually increase the time your pets stay in the same room. But don't let them see each other in private. Over time, this can be done, but at first it is too early.
The most important thing is patience and love. Show your pets that you love them, over time, the animals will also love each other.