SOE have deployed the alpha for EverQuest Next Landmark , which you'll remember is the crafty/Photoshoppy prototype-type thing for their super-voxelly sequel to EverQuest 2. It's not the sort of alpha you can just download, however - you'll have to purchase a 'Founder's Pack' first. The cheapest tier of Founder's Pack with alpha access will set you back a whopping $60, so it's worth having a bit of a think before you decide whether or not to dive in. (Our hands-on preview from way back when might help.) EverQuest Next Landmark will be free-to-play when it eventually releases for real.
Not everything is present in this initial alpha build. Combat, for example, is nowhere to be seen. You can, however, both craft and build stuff, which is likely why you signed up in the first place. If you're worried about character wipes, don't be (much): SOE have told RPS that they'll use character wipes "very, very rarely". Handily, there will be a way to preserve your built objects from the oncoming storm of server wipes too.
Will your PC be able to run it? Probably, but here are the system requirements just in case.