Zagreb to postojna caves

Google Maps knows....

The answer is no, you will stay on the highway that runs south of central Ljubljana. Unless
you want to drive into Ljubljana.

Does it take long to cross the border at customs? Thank you

It shouldn't, but you never know, plus you haven't said anything about date/time
you are thinking of doing this.

If you use Google Maps, then you can find the route that works for you.

Note that as Croatia is now part of the Schengen Zone, there is no longer a required border control between Croatia and Slovenia. You will just be quickly waved through - you will not need to stop at all. By customs, I think you mean passport control as no one cares about customs (the goods you are bringing with you). Your passport will not be stamped or checked.

Thank you very much!

I did a different border cross near Buje and there was a backup since we had to go single lane through a camera check. I later found out that it was an evinjeta check it was not a long wait. I would vote for Škocjan caves instead. It’s just an extra 15 minutes.