Hi Marcus, to the best of my knowledge this depends on the capability of graphics adapter in the laptop, if the graphics card can display 1080p then, regardless of the internal display, your external screen should work in the native camera resolution. Of course, if you mirror the screen then you will be limited to 720p - you need to work with the lowest common denominator.
However, this isn’t a given; if you are importing video via USB then the driver/ intermediary software will have a say in the process. If these guys aren’t playing ball then you could always run the video feed directly into the external display via one of the many converters available on the market (e.g. Composite video - HDMI), there are also converters which work in the digital domain (‘re-clockers’) but your camera needs to have the appropriate output.