It depends on your video card and the source material.
If the source material is not in 1080p, your tv will NOY upconvert it. The resolution of the monitor has nothing to do with the actual content. So called 1080P movies from a P2P are RARELY 1080P. They are usually 720i. Just look at the file size DEAD giveaway! 1080P file sizes are HUGE. You can hook it to your TV and see the digital effects.
If your screen resolution is only 1366 they did NOT put a real vdeo card in your computer. That means you're using integrated graphics which means no real 1080P. It also means that if you try to push it hard, your system will NOT last long. there is a differnce in voltage and current. A mobo of that calible cannot handle current draw of 1080P video for a long time. A laptop with a mobo of that quality will also not have good power regulation, further shortening the life of your system.
One guy mentioned that the hdmi port will handle 1080P resolution and it is true, but the source must be 1080P and the VID CARD must be able to resolve it. if the card can't resolve it, it can't be passed to the port. All the port and cable is, is a CONDUIT to pass data. He obviously just googled the specs of the port without reading your question.
Another consideration is while it is certainly ok to use it to watch a video now and then on that quality computer. The quality of that mobo means it should NOT be done on a regular basis. Even a good laptop mobo from an alienware, and xps or a quosimo shouldn't be used to push a tv for long. And if your screen resolution is 1366, you do NOT have either of those.
On the TV/monitor end. If you have a MONITOR, it will probably be ok, but if you have a TV, the TV preamp will also be stressed and cause your tv to die sooner.
Another issue is that while connected, if you have someone bump into the cable, it will put a strain on your port possible damaging the mobo or causing the laptop to fall over damaging the lcd panel.
Remember damage to the mobo or the screen caused by accident is NOT covered by your hardware warranty. My frineds that have shops report this issue ALOT. I work corporate so I personally dont see that issue, but my friends say they make ALOT of money from people who connect a laptop to their tv.
I am NOT telling you this to put you down. I am trying to warn you so you can save money, so you don't have to buy a new laptop and a new TV or pay huge repair bills. Good luck!