You can't blame yourself, hun. You shouldn't blame hubby because it was just a huge accident.
I don't think it is trivial. People have love for animals just as they do for people.
About if "I had been home", you never know what would have happened. What would you have done if you were the one putting the 'kids' in the car and the baby got away from you? It would still be an accident.
I truly believe things happen for a reason, whether they are big or small things. I cannot say what the reason was for your baby, but know that she is ok.
My step-dad still thinks that my mom wouldn't have gotten sick and gone to the hospital and passed if he had not gone out of town as it was the ONE time he ever left without mom. When he came home she passed. There was nothing he could have done, even if he was home and that is how I think about your poor baby.

I'm so sorry for your loss.

(((((wisewoman)))))