New member - first time towing this week

Hey guys, I'm a new member but have had two tacomas. My first one was a 11 4cyl access cab. Just had a baby recently and found that the access cab doesn't fit car seats.

I now have a 07 DCSB 6 spd mt. No tow package, but came with a class 3 hitch and brake control.

I am going camping next week and renting a small 18' keystone Zeppelin TT. Me and the family will be in Banff national park, so a fait bit of hills.

I have read the towing bible but have some questions.

Since I have a manual, do I still need an extra oil cooler?

I found a Toyota towing guide that says I'm good for 5000# without the towing package (attached), is this true? I assume the 3500# is only when using the bumper.

Let me know if you guys have any other tips.