I run OS 9 on 1920x1080 and 1920x1200 all the time. In fact, at this very moment I have two OS 9 computers set up and both are connected to LCDs running those respective resolutions-a PowerMac G4 w/Geforce 4Ti on a 1920x1080 generic monitor, and a PowerMacintosh 9600/200MP with a Radeon 9200 connected to a 1920x1200 ADC acrylic cinema display.
I've gone as far back as System 7.5.5 on 1920x1200.
I've also done 1920x1080 or 1920x1200 in OS 9 from a 2MX, Geforce 3, Geforce 4MX, Radeon 9000, Radeon 8500, Voodoo 5, and probably a few other cards I'm forgetting.
What GPU are you running? Some OS 9 GPUs don't play so nicely at that resolution. Otherwise it should work with no issue and without the need for any external software. Apple marketed a 1920x1200 display that would work perfectly with computers that booted OS 9 natively at that resolution.