Hi Stephen,
hopefully it’s just me, but I can’t see the image you uploaded. But I think I have a solution anyway.
Expand the dot on the timeline so you can see the position, then expand the camera transform properties and use the Point of Interest pickwhip to link the camera’s POI to the dot’s position. This means the dot will always be in the center of the screen.
If your dot is parented, then you might need to create a Null Object and set its position using this expression:
L=thisComp.layer("Dot");
L.toWorld(L.anchorPoint);
This gets you the comp coordinates for a parented object. And then use the Camera POI on the null layer. (Thinking about it, you could probably just use the above expression on the Camera’s POI instead of bothering with the null.)