Yes, it's normal.

The oil light works by pressure. and would not go on till the pressure drops below a certain level (somewhere around 20 psi).

It has nothing to do with the level, unless that gets so low that the oil pickup can't suck in any oil. Then you're really in trouble.

Is this your first oil change sine purchasing? If so, I would change the filter, add 1/2 can of motor flush (following its' instructions) , drain all the oil and change the filter (yes, again) and refill. also install a new pcv.

The reasoning behind this is that since the oil was so low, it was extra dirty and caused the filter to work harder and become dirtier. It could also contribute to varnish or sludge in the engine.

While you're at it , replace the pcv and check your oil level at every other gas fillup. Watch for excessive oil consumption.