It's never too early for a good track day. Take the Motorcycle Safety Foundation beginner course (or your country's equivalent) but 6 months of riding means you should be comfortable enough on your bike to get on a track, in the right environment.
I did my first one last fall, and I wish I'd done it sooner. I learned more about the handling and capabilities of my motorcycle in 2 days than I did in the previous 18 years of street riding, reading books and magazines, and watching videos. I learned a lot the first two years I rode also, but that involved crashing repeatedly.
Choose an organization that offers a track school as opposed to a pure track day. I went with Sportbike Track Time and their Novice class has a (required) classroom component and a good ratio of instructors/control riders to students. There were some real noobs out there, but the organizers did a great job making sure everyone rode at a pace that was comfortable for them, even if it meant one really slow girl got her own instructor.
Join a local riding group and make some friends. You'll likely need help to get to a track day; a support vehicle to carry tools, gas cans, and a cooler is necessary. It's also nice to haul your bike on a trailer, or at least have trailer space available if your bike needs help getting home. There's no more reason you should crash on the track than on the street, but it's possible, so it's good to have a plan.
You'll need full gear - real motorcycle boots, gloves, leathers either one-piece or zip together two piece, spine protector, and an undamaged helmet. Some groups allow textile suits in Novice, so check with the groups that hold track days in your area. You should be riding in full gear all the time anyway, so it's money well spent.
You'll also need a motorcycle that can pass the tech inspection - everything in working order, new or nearly new tires, no knackered chains or worn out brake pads. You _don't_ need a new sportbike. Most track groups have a minimum CC requirement, but you can learn to ride anything better on a track. The day I went there was a guy out on an old KZ650, and I and another guy were on '86 VFRs. Depending on the track and class you may need to replace your coolant with water. The one I went to didn't require safety wire or coolant replacement in Novice, just tape over all glass, wheel weights, and fold in the mirrors.