$1280 for the timing belt cover gasket job, even if it also include crank seal replacement, seems a tad on the high side. But not totally out of the ball park. I expect there are other things they plan to do at the same time – not an unusual thing once the stuff is all taken apart anyway. Maybe the water pump, who knows.
But maybe what you are really looking for here is advice to a slightly different question:
"If I need a repair costing close to $1500 on a 12 year old Corolla with 130 K miles, and I need a car that is bullet-proof reliable and one that would seldom if ever need repairs of that cost, should I buy a new Corolla? "
I think the answer to that is “yes”. A new Corolla is probably the better choice for you. Your 2003 Corolla is a pretty reliable car as used cars go, but it will never be as reliable as a new Corolla.
A 2003 with only 127k miles would certainly be worth fixing. Agreed that you should get another opinion and estimate. I’m assuming by the price quote they’re replacing the cover gasket and if it were my car I’d throw a new timing chain set on it while the cover is off.
It seems a bit unusual for a timing cover gasket to leak on a comparatively low miles Toyota so I have to wonder if the problem may be a leaking crank seal which is more of a possibility and whose replacement cost should be much, much less than a cover gasket.
Leaks can happen but aren’t serious where your fictional leak is located. If you can’t find oil on the road or garage floor, there is no problem to fix. $1,200 is a large bonus for finding a worn belt.