We are truly sorry to hear about your dog's health condition. We believe that God cares for all His creatures, and we understand the bond between you and your pet. But the Holy Scriptures are clear that God answers prayers according to His will and in Jesus name. The verse you're referring to says, "Again, assuredly I tell you, that if two of you will agree on earth concerning anything that they will ask, it will be done for them by my Father who is in heaven. For where two or three are gathered together in my name, there I am in the middle of them." Matthew 18:19-20 WEB.
First, we want to remind you that God hears the prayers of those who come to Him through Jesus Christ. It's important to pray in Jesus' name, as He is the mediator between God and man. "For there is one God, and one mediator between God and men, the man Christ Jesus," 1 Timothy 2:5 WEB.
We also need to clarify that God's promises and the power of agreement in prayer are intended for His children, those who have believed in Jesus Christ. While we can empathize with your concern for your pet, we must focus our prayers on the healing and salvation of people, as this is the primary concern of God's kingdom.
However, we can pray that God would give you peace and comfort during this time, and that His will would be done in this situation. Let us pray together:
Heavenly Father, we come before You in Jesus' name, lifting up our fellow believer who is in need of Your comfort. Lord, we ask that You would give them peace and strength during this time, as they care for their pet. We know that You care for all Your creatures, and we trust that You will act according to Your will and wisdom in this situation. Help us all to keep our focus on You, and to trust in Your unfailing love. In Jesus' name, we pray. Amen.
We also encourage you to seek God's will in all things, and to continue to pray and study His Word. If you have not already, consider committing your life to Jesus Christ, believing in Him as your Lord and Savior. "For God loved the world so much that he gave his one and only Son, so that everyone who believes in him may not perish but have eternal life." John 3:16 WEB.