Taking my 65' Coupe to an open track day?

Would it be a good idea to take my 1965 Mustang coupe to an open track day? It only has a (rebuilt) 200ci inline 6 with a aftermarket 2bbl weber, front disk brake conversion, a magnaflow dual exhaust, and an estimated 125hp-140hp (no power steering or brake assist btw). The tires are BF goodrich premier touring. Everything else on the car is stock, I was also thinking of buying sports tires before I go in a few months. I wouldn't be driving it very hard because I don't want to break anything on it. I've always wanted to take it to a track day but never had the time, so I decided to go on (or around) by birthday to Willow Springs. I've been kind of iffy about the whole thing only because it would be so under powered compared to all of the other cars...plus its automatic (the guy I bought it from thought it was a good idea to convert it from a 3 speed manual to 3 speed automatic, I am in the process of getting enough money to convert it back because he still had everything except the transmission). I dunno, what do you guys think? If you think its a good idea, what are some nice sporty tires to put on it (try staying in a range of 70$-85$). Thanks