There is nothing wrong in training dogs for essential purposes such as hunting, guiding the blind, guarding houses or sheep, and serving in the police force. Hence, gaining money for this work is also permissible and lawful in Islam.
Sheikh Ahmad Kutty, an Islamic scholar from Toronto, Canada, stated,
Almighty Allah tells us in the Qur’an that humans can use animals such as dogs for beneficial purposes by training them: (They will ask you as to what is lawful to them. Say: “Lawful to you are all the good things of life. And as for those hunting animals which you train by imparting to them something of the knowledge that God has imparted to yourselves – eat of what they seize for you, but mention God’s name over it, and remain conscious of God: verily, God is swift in reckoning.) (Al-Ma’idah 5: 4)
The animals mentioned in the above verse include dogs as well all other animals used for hunting, like a hound, a falcon, and a cheetah.
We can infer from this that dog training is a service you can render and receive a payment for; as it is no different from any other skill that is acquired since it takes practice and effort. Therefore, you are allowed to receive a payment for your services in training and taking care of the dogs.