Ok, after the head fell off the 1st one (yes i did cry 
) I was depressed and feeling defeated. it was my 1st cake disaster.
But i got over it and made another one!! This time i baked the dowel rods INTO the cake. 
Not sure it that is done or not, but since it was for family, I didn't care. I just wanted to make sure the head didn't fall off this time!
I've been doing the traditional lamb cake for our family get together for the last 7 or so years. My grandma made it for as long as I could remember until she passed it on to me.
I have had two have their heads fall off. One was when I was icing it. I had iced the back out of the head and went to do something and came back and the head was laying there. Last year the already decorated lamb did not make it to the lake (super bumpy road) with his head attached. It was a little wobbly, so I took icing with me since I had a feeling it would happen. Some toothpics and icing and it looked okay.
This year I took the lamb naked and iced him when I got there. The lamb cake pan I have makes a thinnish neck that often wobbles, one of those evils of the pan. So it was probably a case of the cake having issues and not anything you did wrong.
Sorry you had problems with it. 
But now you have your first cake disaster out of your way. Don't let it hold you back from making other cakes. 
Not long after I started decorating I had the same thing happen. I didn't know much about doweling cakes then. I used drinking straws. Had some problems when I was decorating but I thought I had it put together well enough. That was until the next morning when I got up and the head was laying in the box beside the body. I really freaked out then but it is pretty funny when I think about it now. I returned the pan to Wal-Mart and told them it was defective (ha). Anyway I refer to that disaster as my "sacrificial lamb".
Quote by @%username% on %date%
%body%