Can't see any benefit in turning a dipole on its side at 1090 MHz. There are properly designed (commercial & build yourself) verticals available that will give better results. With a vertical at these frequencies it's quite easy to simulate the ground plane using very short radials , in effect that's what the metal plate on the supplied antenna is doing.
Dipoles (H mounted or V) have big nulls in them and little overhead coverage.
Bear in mind the signal transmitted will be vertically polarised so you may suffer phasing losses if trying to receive it on a horizontal.