Can I trailer cars with my 80 chevy k10?

[zieg85]

The other numbers that you mentioned are camper loading.  If you have a string of 3 digit starting with a letter, second digit is either a letter or number followed by a number... Those are RPO #'s which is what your truck originally came with.  That list is available here 
http://www.chuckschevytruckpages.com/rpo_codes_1973-87.html 

[Irish_Alley]

As long as you got brakes on that trailer you can haul anything you don't need a special license for

[beastie_3]

How often do you plan on towing?

[Cheyenne]

Thanks everyone again.. I would haul a car maybe once or twice a month in the winters she be parked

[fitz]

In general your truck will do fine. Others have covered the basics. Tranny cooler and electric brakes are a must.
My only concern would be your 1/2 ton rear end (regardless if it's a 10 or 12 bolt).
That is 1 area I would upgrade. my first choice would be to upgrade to 3/4 ton units but at the very least I would add an Eaton posi.