Candy, Like Dave said, the element is supposed to be [smiley=cherry.gif] red when it's on a heat cycle. Depending on the setting, it should cycle on and off as needed to maintain the temp in the barrel. First thing to check is as Dave mentioned....often the discharge vent is stopped up, so if you can see into it after removing it from the back of the dryer, check that out...if it's like most, it will exit through a wall with a little angled cap on the outside to keep the weather out, so make sure there are no obstructions to impeed the air flow...kind of like on our scooters. One way to test this would be to unhook the vent tube from the back of the dryer and let it run unobstructed to see if that still trips the breaker. Depends on where the dryer is located though as to whether you can stand the added heat to that rooms environment. It won't hurt anything to do this for a while to test. Did you notice your clothes being unusually hot when you pulled them from the dryer before this tripping the breaker thing started? If so, you've got a bad t'stat, or temp sensor.
Hopefully, the dryer is on it's own circuit (it really should be). Breakers can get weak over the years. Has anything been added to your home recently that might have caused someone to (wrongfully) tie into that circuit? Breakers are pretty cheap, but if Jamie is not comfortable changing that out, don't let him try.
The bottom line is if the dryer is over 10 years old, and you've been wanting another one anyway, it's a good excuse. I'd at least find out what's wrong first, then decide on whether it's worth fixing.