I know, I know. Your first instinct is to jump on Reddit or some grief forum and find "the right" way to handle it. Don’t. There is no right way. You might feel numb, angry, or guilty for not being "sadder." All of that is totally valid. You are allowed to ugly-cry into your dog’s old blanket. No judgment here.
Your brain will try to rationalize it. "It was just a dog." I’m going to stop you right there. It was never just a dog. It was the witness to your worst haircut, your biggest mistakes, and your quietest victories. Honor that history by letting yourself be a mess for a day or two.