Your Toyota remote works at a frequency of 303.875 Mhz
If this is true, then a one-wire antenna length can be calculated by 300/303.875 = .9872 meters or 98.72 cm in length. I would bet cutting a wire to 1.1 meters and running it up the B pillar and across the top of the DS door would be just fine. Start at 1.1 meters and trim off a couple centimeters each time testing for range until it starts to get less and stop.
Another thing to try would be to grab a piece of coax cabling like the stuff used for cable TV. Cut a length long enough to get to the B pillar and above the bottom of the window PLUS the 1 meter for the antenna. If you solder the shielding to the ground on the alarm unit and replace the gray wire with the center wire in the coax, then strip all of the insulation and shielding down to just the bare center wire starting above the bottom of the DS window and then run the wire up the B pillar and along the top of the DS door and down the A pillar you'd probably maximize reception. The shielded/grounded coax section acts as a wave guide for the received radio signal. The bare center wire is the antenna part. Doing things this way means the entire antenna is above the bulk of the metal door skin and only has the pillars and roof skin attenuating the signal. I would bet that the resulting range would be HUGE with this setup.
I'm going to try it out on my LX this weekend.