In reply to tingle:
There's no snow on Fuji yet in September, and in many ways it's a nice time of year to go... Far less crowds on the mountain, and the buses to the 5th stations are still running. If you're walking up through the night it can get cold, so don't go 'too' light... at least make sure you've got a few warm layers each.
The main drawback to September, maybe the only one, is that it's typhoon season in Japan and can be very wet. That doesn't mean it will rain every day, but this year in particular has been extremely wet. So you might want to build some flexibility into your schedule during the month, keep a firm on the weather forecasts (
http://www.mountain-forecast.com/peaks/Fuji-san/forecasts/3776) and be prepared to head over there as soon as you get a couple of dry and clear days.
Feel free to get in touch by email if you want any more info about it, and if you and your girlfriend might be looking for any other hikes or rock climbs to do while you're over here, you might find my book ("10 Classic Alpine Climbs of Japan" -
http://amzn.to/2cZRIrU) or site (Climb Japan) useful for ideas.
Enjoy planning your trip! Tony