Getting a permit is easy this time of year -- It's October, and snow is falling on the trail as I write.
Just understand, Whitney is a step above Half Dome. The trail head STARTS at the elevation of the Half Dome summit.
If you and your gf are in really good shape, you might be able to make a day hike. All you need to do is drop into the Visitor Center S of Lone Pine and ask for a permit. The walk-ins are free, and there will always be some, since many people will drop out due to the conditions.
Good luck! But most of all, be safe. And remember, the mountain will always be there.