[Humabout]

Something else to consider:

Lasers aren't instant-speed-of-light weapons. They have to send some sort of initial ranging pulse so they can adjust their focal array so that the laser beam is at maximum focus on the target. This takes 2 * [Distance in Light-Seconds] / [1 Light-Second per Second] to range the target and fire the weaponized laser. The weaponized laser then takes another [Distance in Light-Seconds] / [1 Light-Second per Second] to reach the target. Adding these and simplifying units, we find that it takes 3 * [ Distance in Light Seconds ] seconds to from pressing the fire button to the target getting hit. That generally won't be much time, but space is big and ranges might be large. Let's see what sort of limits exist for ability to dodge.

The target can probably detect the ranging ping (or it's really in for a cruel surprise), so let's just assume it can. This gives the target 2 * [Distance in Light-Seconds] seconds between getting pinged and getting hit. That's how long the target ship has to react to the ping and dodge.

Next, let's take a look at two cases: (1) Human doing the dodging and (2) computer doing the dodging.

(1) Human Dodging.
An average human takes about 0.25 seconds for visual stimulus, 0.17 seconds for audial stimulus, and 0.15 seconds for tactile stimulus, as per random Google result I'm not taking the time to vet. It doesn't sound horribly off. That suggests that depending on the warning system, the pilot will have different lengths of time to react and dodge. This mean that any shot within 0.25 light-seconds for visual warning, 0.17 light-seconds for audial warning, or 0.15 light-seconds for tactile warning probably shouldn't allow any dodge that requires pilot input other than general evasive maneuvers.

(2) Computer Dodging.
This is very hardware and software dependent. Currently, (by similar unvetted Google search), computers are alleged to have comparable reaction times as humans, but you don't have TL 8 computers. You have high-TL sci-fi computers, so can probably set this arbitrarily fast, meaning a computer can always attempt to dodge a laser weapon.

Next step is factoring in the responsiveness of the ship itself. This is quite a bit harder to do, since it is so very dependent on the specific ship. Here, you probably want to just pick a number of seconds that sounds reasonable. - you mentioned humans dodge 3 * Height, so that's one measure. But really when you think about it, the ship never has to move more than half it's longest dimension get out of the way of a shot. How long does this take? That's pretty simple:

t = sqrt(2 * distance moved / acceleration)

or for our purposes

t = sqrt{[Ship Length in Meters] / (9.81 * [Ship Acceleration in Gs])}

We add this time to the reaction time of whoever is dodging to get the total time to dodge. If this is less than 2 * [Distance to Target in Light-Seconds] seconds, the target can attempt to dodge. If not, the target just gets hit.

It's also worth noting that a spaceship can simply rotate out of the way, as well, but this is very geometry-dependent. At best, it's nearly instantaneous, and at worst, it takes too long. That sounds silly to mention, but GURPS doesn't give enough details to narrow the domain any further. It does, however, provide you with a way to fudge numbers in the target's favor, if that's the flavor you want.

WORKED EXAMPLE
A SM+12 ship is 200 m long and has a maximum acceleration of 1 G. This means that it takes the ship

t = sqrt{[200] / (9.81 * [1])} = 4.52 seconds to clear a worst-case attack.

Let's assume it is piloted by a human receiving visual warnings of inbound attacks, resulting in a 0.25 second reaction time. This means the target needs at least 4.77 seconds of warning to have a chance of successfully dodging. We know the target has 2 * [Distance in Light-Seconds] seconds to dodge, so we can then set this equal to 4.77 seconds to find that any shot fired within 2.385 light-seconds or 715,005 km has a chance to prevent the target from dodging a shot aimed at the dead middle of the ship. At the other end of the spectrum, a shot fired at the very edge of the end of the ship would need to have a range of 0.125 light-seconds or 37,474 km to deny the pilot time to even react.

Note: A computer wouldn't have that reaction time to worry about and could always dodge, and could dodge a hit amidship fired from beyond 2.26 light-seconds (677,531 km) or any shot at its extreme edge. This suggests AI have the advantage at close ranges, but aren't necessarily superior at longer ranges.

Also, This assumes the attacker already knows of the target's existence. Add another [Distance in Light-Seconds] seconds to find the time from detection to hit, assuming the attacker fires as soon as the target is spotted. Add 2 * [Distance in Light-Seconds] seconds to the target's allowable reaction time if the target was detected via active sensors and detected the ping (probably a safe assumption for military craft).

[EDIT]
And having written all of that, I realize that it ignores the "Dodge includes moving erratically to avoid being hit" thing. It does, however, provide a hard line where Dodge no longer can represent an actual reaction to an attack. If you don't mind the added complication, you could apply Restricted Dodge Against Firearms from Tactical Shooting, p. 17 with awareness determined by range to target as shown above. And those range thresholds can be pre-calculated for ships, so you don't have to do them on the fly.