The only possible bottleneck is the laptop's natural resolution. If it is below 1080, but your desktop monitor is 1080, the output to the desktop monitor will be limited to the laptop resolution. The desktop monitor can be 1080 in this case, only if the laptop screen is disabled.
I haven't played with latest laptops for a while, as my two laptops were 6,7 years old (all dead by now, although I will try to restore one this weekend), so my statement above is limited to the laptops up until a year ago with IGP that I helped my friends tweak . Not sure about the current generation laptops, and/or with discrete graphics.
EDIT: With separate graphics card, you may output different resolution to the external monitor. Right now my desktop is connected to 1440 x 900 and 1920 x 1080 monitors with their natural resolution, the former via motherboard DVI connector using HD 2000 IGP, the latter via GTX 560 Ti 448 Core DVI. Why not with a laptop, if it works in desktop?