We are truly sorry to hear about your dog's condition, and we appreciate your faith in God's healing power. We are reminded of the verse you mentioned, and we want to share some additional scriptures to encourage you in this difficult time.
Firstly, we want to address that we are not to put our trust in anyone or anything but God. We are not to pray to angels, Mary, or saints. We do not pray in their name, but only in the name of Jesus Christ. No one comes to the Father but by him. The Bible says,
For there is one God, and one mediator between God and men, the man Christ Jesus. 1 Timothy 2:5 WEB
Be it known unto you all, and to all the people of Israel, that in the name of Jesus Christ of Nazareth, whom ye crucified, whom God raised from the dead, even in him doth this man stand here before you whole. And in none other is there salvation: for neither is there any other name under heaven, that is given among men, wherein we must be saved. Acts 4:10,12 WEB
And whatever you will ask in my name, that will I do, that the Father may be glorified in the Son. If you will ask anything in my name, I will do it. John 14:13-14 WEB
That being said, let us pray together for your dog.
Heavenly Father, we come before you in the name of Jesus Christ, lifting up this beloved pet to you. We ask for your healing touch upon her, knowing that nothing is impossible for you. We pray for wisdom and guidance for the veterinarians treating her, and we ask for comfort and strength for her owner during this challenging time.
We stand on your Word, Lord, which says, "For I know the thoughts that I think toward you, says Yahweh, thoughts of peace, and not of evil, to give you hope and a future. You shall call on me, and you shall go and pray to me, and I will listen to you. You shall seek me, and find me, when you search for me with all your heart." Jeremiah 29:11-13 WEB
Lord, we search for you with all our hearts, trusting in your goodness and mercy. We ask for healing and restoration for this precious animal, in Jesus Christ's name. Amen.
We encourage you to continue trusting in God's goodness and mercy. Remember that he cares for you and your pet, and he is always with you, no matter the outcome. Keep praying and seeking his face, knowing that he hears your prayers and will act according to his perfect will.
"Are not five sparrows sold for two assaria coins? Not one of them is forgotten by God. But the very hairs of your head are all numbered. Therefore don't be afraid. You are of more value than many sparrows." Luke 12:6-7 WEB
"Come to me, all you who labor and are heavily burdened, and I will give you rest. Take my yoke upon you, and learn from me, for I am gentle and lowly in heart; and you will find rest for your souls. For my yoke is easy, and my burden is light." Matthew 11:28-30 WEB
Prayer Focus: God, Thank You for loving me. God, I ask You in Jesus’ name please bless me with everything that I stand in need of and everything You want me to have. 
