My 1981 vette headlight doors open one at a time and slowly . Is this normal ? 

Staggered opening is not unusual as it is depending on different friction levels and spring constants. However depending on the degree of slowly, you may be suffering from a vacuum leak.

Vacuum system seems to be intact with no leaks .

I guess my question is " is it normal for one to open before the other ? "

Any advise will be greatly appreciated. 

Mine certainly don't come up in unison. More like a quick clunk, clunk.

How long does it take for them both to be fully open from the time you turn them on?

On my '75, the driver's side opens first, then about 2-3 seconds later, the passenger side opens; both with the clunk, clunk.

Depending on vacuum build, and condition of the canisters, they will very in opening times. With no, or very little loss,  they should open pretty much to together. Closing times will be the same. 

They are designed to open together however age and friction loss will slow one down more than the other.   Reduced vacuum is another contributor and is the down-side of engine swaps or changing to a performance cam.  As long as they get open and on, go with it.  DJ