First, Don't blame yourself. It's so hard to keep our dogs from doing things which will hurt them. I would have never thought the dowel would cause this terrible damage.
Every night when I pray, I ask God to keep my dog from getting into anything which could hurt her. Our dogs are SO smart but not quite smart enough to stay away from things bad for them.
I'm so sorry for the pain you are feeling now. It will never pass completely but will get better and lead in to great memories. I'm on my third black lab, she's a hoot and everyday I remember my first two and the fun we had.
bless you both
"I ain't here for a long time, I'm here for a good time"
King George Straight