So I was thinking of moving to Fedora. It has been long known for stability,
I have never seen anyone refer to Fedora as stable before so would agree with chrism01. Using Fedora, you are basically a beta tester for Red Hat. Frequent releases and short term support are not going to contribute to stability so if that is what you are looking for, Slackware, CentOS and the other recommendations above would be much better.