Rewriting to avoid "had had" is almost always a good idea. It reads even more terribly than it sounds.
The easy way out is to use a contraction:
I'd had enough of this nonsense and was ready to move on.
...but that's a little cheap. Depending on the context of the quote, you have several options:
Having had enough of this nonsense, I was ready to move on.
I was fed up with this nonsense and ready to move on.
"Damn this nonsense and twirl my whiskers," I said, fully prepared and capable of moving along.