As long as you stay reasonably below the rating on the inverter you plan to purchase, you will be fine. They have both a peak and a continuous rating. You need to stay below the continuous rating. The peak rating is for starting up equipment, when power draw will be highest, and can be sustained momentarily.
The circuits in your car are fused for good reason. Only if modifications to your car have been made should any of your circuits be unfused. This is your responsibility to determine. If you overload your 12V accessory outlet, it'll blow it's fuse. If you overload the inverter, it'll blow it's fuse or trigger it's circuit breaker.
While a lot of inverters do not produce the cleanest power output, as in, a clean sine wave, most laptop power adapters are quite tolerant of what will be produced and will run just fine. The power adapter for the laptop will buffer any bad power from the laptop. That's it's point. To take the input power and output just what the laptop requires to run. If the inverter cuts out, the laptop will automatically run from it's battery, so it isn't as though you are unprotected in that regard.
When starting the car, it's possible the inverter will lose power momentarily. Also, an alternator in the charging circuit of an automobile can not supply peak power when at idle, so if you manage to have a high draw through your inverter, it may not be able to supply the rated output at idle. Being that the particular inverter you are interested in is powered from a 12V accessory outlet (cigarette lighter adapter), the draw should be low enough you don't encounter this problem. I've usually only seen the issue with inverters that were large enough you had to wire them directly to the battery.
If your 12V accessory outlet in your car is always on, don't forget to turn your inverter off, or unplug it, when not in use and the car is not running. Your inverter will consume power, even with nothing plugged into it, and will eventually drain your car's battery if left unattended.
I've run laptops for years off of various inverters and see no major concerns there. It's nice to have some 120V outlets on hand wherever you are, as not every device has a 12V option.