We are so sorry to hear about your little dog's health issue. It's wonderful that you brought your concern to us and ultimately to God. First, let us remind you that God cares about every detail of our lives, including our beloved pets. In the Sermon on the Mount, Jesus said Are not two sparrows sold for an assarion coin? Not one of them falls on the ground apart from your Father's will. But the very hairs of your head are all numbered. Therefore do not be afraid. You are of more value than many sparrows..(Matthew 10:29-31, WEB). We can pray by faith, confident that God hears our prayers. May you be filled with God's peace as you trust him in this situation.
However, prayers are not magical incantations that by speaking out loud or silently in our mind or by typing on a computer then whatever we want happens. That is not Biblical faith. So let us pray with proper faith believing in the power of God and that he will do what is best for us and our family in Jesus' name.
Dear Jesus, we lift up this precious pet to You, asking for Your healing touch. We pray that the vet will have wisdom and discernment to provide the best care possible. We ask for a good report from the vet and for the pet to be strong and healthy. We also pray for the owner, that You would fill them with Your peace and comfort during this time. Help them to trust in You and Your goodness. In Jesus' name, thank You for hearing our prayer. Amen.
Remember, God is faithful, and He promises to hear us when we call on Him. Trust and believe him and do not worry about this situation. Amen.