I'm sorry your friend was so insensitive; I suspect she's never had a pet or been in your situation. But I understand your feelings, because I grew up with animals on a farm, and we've always had dogs and cats that seemed like part of our family. When King David was told about a pet lamb that was taken from its owner, he became very angry; he knew how much a pet can mean to someone (see 2 Samuel 12:1-6).
It's true that animals aren't the same as humans, since they don't have souls the way we do. But that doesn't mean God doesn't care about them. After all, He created them, and He watches over them. Jesus said, "Are not five sparrows sold for two pennies? Yet not one of them is forgotten by God" (Luke 12:6). God also reminds us that "every animal of the forest is mine, and the cattle on a thousand hills" (Psalm 50:10).
God knows our feelings, and He cares when life's hurts come upon us (as they will). Thank Him for the memories you have of this pet, and ask Him also to help you see beyond your own hurt to the hurts of someone who needs your friendship.
Most of all, I pray that this may be a time when you and your family strengthen your relationship with each other—and with God. Life is short, but ahead of us is an eternity in heaven when we know Christ. Is your hope in Him?