All depends on how much your trailer weighs. I pull my TJ behind a 1500 Yukon with a fairly heavy trailer and it does alright. With the 305 as long as your trailer is fairly light you should be ok. You wont set any land speed records though. You will definantly want good breaks on the trailer. Your biggest issue will be getting it all to stop.
What year C-10 are we talking about? You should be ok. I ould not try to flat tow it though. Make sure you have brakes on your trailer. I have even seen tow dollies with brakes if you go that route. Get a good controller, the prodigy 2 would be good and the price is right.