Think also about someone bumping into it while under the plane. Doubler could save the skin from creasing at the edge of the Ant.
If you mount it close to a supporting structure, like between floor ribs, you should be able to do away with the doubler.
I've got two whip antennas under my seats that have no doublers. IIRC, I used the same setup on my 1st 7 and flew about 500 hours with no issues prior to selling it.
Why add the weight if the ribs provide a solid base for the skin on which the antenna mounts?