If you are current on your maintenance, have SELinux and the firewall enabled (the default configuration), you are as secure as you can be, without actually getting into the security details. Fedora is a leading edge security oriented
distribution, and has just about every security layer imaginable. I have been running Fedora Since FC1 (and Red Hat since 4.2, 1997).
My machines are under continuous attack, as are most machines with web sites and ssh access. I monitor continuously. No attack has ever successfully penetrated - but do make sure you have secure login passwords (see 'man pwgen') and don't make any changes to allow remote root logins.
While there are currently about 120,000+ virus, trojans, worms targeting Windows systems, there are less than two dozen targeting Linux systems. The only way you can be safer is to unplug your network.