As long as you're aware of the pitfalls of a 370Z in stock form on the track and don't push them and you've kept up with regular Z maintenance for the 135K miles, I say you're good to go
Back off when the car starts pulling timing (oil temps > 250 on the gauge). Probably best to end the session and cool off before next one.
Avoid threshold braking. Some fresh brake fluid would be a good thing to do prior (recommend Motul RBF600).
Watch out for fuel starve - keep the throttle input minimum during right hand turns with lots of centrifugal force.
If the clutch is still the original stock one, be easy on it.
You can have a lot of fun on the track in a stock Z just cruising at the Z's comfort level. But if you are pushing for fast times or driving really hard, chances are you're going to break something or at least encounter some limiting factor of the Z in stock form.
I had my Z out at COTA a number of years ago when it was my DD - mostly stock as my only mods were an Ecutek tune and R2C intakes. It was fun, but I went a little hard and had to stop my session early.
Now I'm over 100K and looking to take it out to the track for hard driving. But I'm having to spend a lot of money to make sure that it will be reliable so I can drive it to the track, drive it hard on the track, and drive it home from the track.