detect the laser dot and find a way to calculate the coordinates
I like your idea, but there's some aspects of it that would make it difficult, at best, which perhaps you hadn't considered.
Laser range finders are an off-the-shelf item that you could either buy or mimic the sop for and incorporate into your drone,
BUT in order for that to work the "target" must be able to reflect the light BACK to a sensor.
Laser designation is relatively easier: It's basically a souped up version of the simple "line follower" robot/toy (but reversed).
In the toy three sensors are used which look at light/dark. When the center sensor see no light (the dark line) no steering input is given.
When the left sensor sees the line it generates a "steer left" command until the line is centered again; similar routine for the right side.
This way the toy stays centered on the dark line and keeps following it. Advanced laser designation uses sensors to steer the missile or whatever by the same method but centering on the light instead. Also, they use a camera instead of individual sensors.
The software for following light using a camera is basically just tweaked visual motion detection, another off-the-shelf item.
The way a camera "notices" motion is by variations of the luminance levels within the frame changing. You could hack or mimic that function which moves the camera to instead supply FC inputs to keep the "target" centered in the quad's camera as it flies towards the light.
Position identification could be a simple as the quad's telemetry link giving you the GPS coordinates once at the target.
IF you really wanted to complicate it though (to do as you originally thought) you'd also have to use a compass in the system for heading data too. Basically, knowing the point of origin (the binoculars with laser) in GPS coordinates, with the heading and distance
from that point being known, you COULD calculate the GPS coordinates for the drone and just have it fly to the target that way.
OR the life guard could just fly an ordinary drone close to there LOS then exactly to there FPV and drop the flotation device (without needing any other complicated stuff ) using any unused radio channel