I'm installing prefinished 3/4" white oak (5' width) wood flooring in my bedroom. The bedroom is 19'x18'. I live in New Hampshire and this September has been one of the most humid Septembers on record (as it probably has been in many areas of the US). Now that I'm ready to install, I'm not sure if I should leave much of an expansion gap?

The wood has been acclimating in the house for a month, and probably has absorbed much of this high humidity (as I don't use a dehumidifier in my home). Normally, the best practice is to leave 3/8" around the perimeter of the room to allow for expansion, but in this case isn't the wood at full-expansion already, and it will only shrink once we move into the low humidity winter?

My concern is leaving the expansion gap, and then having the wood flooring shrink during the very dry winter, exposing gaps between the floor and the 1/2' base molding. I suppose I could just use another piece of molding to hide such a problem - but thought I would pose this question to the 'experts'.

A 1/4 expansion gap should be perfectly fine .The real issue will be in the field of the floor if things expand or shrink .To predict this , I'd ask what is this room over ? A basement (finished or unfinished ) a crawl space or is this on a second floor of the home ?

The bedroom is over a finished basement that doesn't have much of a moisture issue as it has a walkout slider door and a bunch of windows.

Each plank will shrink independently of the others. You may have small gaps between rows as the humidity lowers and moisture content of the wood lowers.
If the boards were a floating floor you may see a greater gap at the edges of the room when the flooring dries out in the winter.

I wonder how you have been acclimating the flooring. Is it all out of the boxes? Is it all exposed to air movement? Sometimes people just open the ends of the boxes and think that the wood will acclimate. Pe-finished wood will take longer than unfinished wood.