Koala, I drive a Honda Fit, which had 109 hp when new. This car is exactly what the Civic used to be (I had a couple of late 80s Civic hatchbacks). The Civic has gotten bigger and heavier... it now fills the niche once occupied by the Accord. The Accord has become a full-sized sedan, like the old Ford Taurus.
My car easily hauls my bike and everything I need for a track day... and I don't skimp on the creature comforts. Your car is absolutely able to do the job.
BUT (and it's a big but), to do this you need to be able to store the trailer somewhere. I've got room in my yard to do so, but not room in my marriage. So that narrowed it to basically two options: The $$$$ Kendon folding trailer or the cheap-but-crappy Harbor Freight trailer. Obviously I went for the latter, used, with a ramp. It folds up and sits against the back wall of my garage. Simple.
I believe you don't have the luxury of a place to keep such a thing. That leaves you three options: Rent something, bum a lift, or ride your bike to the track.
Riding to the track: It can be done, but it's not ideal. For one thing, there's the risk of getting stranded if you bin your bike. For a first-time track rider with even an ounce of common sense (which you definitely have), this is very unlikely. The other drawbacks are limited ability to carry stuff that would be nice to have, and the fact that you've got to ride home at the end of the day when you're tired. None of these are deal-breakers. This course is a real option if all else fails.
Bumming a lift: One of the best options, especially if you're not prepared to commit to doing more track days in the future. Contact your track day provider and find out if there's anyone in your area you might be able to connect with. Make calls. Make friends. As I'm sure you saw when you visited Mid-O, track riders really are nice folks who are happy to help, ESPECIALLY helping out new riders. Hell, if I were in the area I'd haul your bike for you for free, just to see you get to the track. There are worse ways to spend a Saturday than helping someone out.
Renting: The big benefits here are that there's no lasting commitment and you're not dependent on anyone else for transport. Your choices here are a whole vehicle or a trailer that you can tow yourself. Pros/cons: Vehicle rental is EXPENSIVE. It'll probably wind up costing more than the track day itself by the time you're done (those mileage charges are killer). Trailer rental is much cheaper (U-Haul motorcycle trailer is $15/day, and you'll likely need it for three days... pick up day one, track day two, return day three). However, you'll need a hitch. This is easy... hit up etrailer.com. A couple of hundred bucks for the hitch and associated parts and about an hour under your car and you're all set.
PS: Re ramps. IIRC you've got a sloped driveway. Good practice for loading... get used to power-walking your bike up and you'll be good to go with a ramp. If you do buy a ramp, get a wide one, and the longer the better... I got mine from Tractor Supply and it's the full width of my trailer. That's really handy. Securing ramp to trailer or vehicle is simple... just run a strap from a solid point on the trailer/vehicle to a point on the ramp so it can't slide off. My ramp even came with the straps and hooks.