Gday mate, its not a straight 12 volts thats going into your computer. The power supply will probably up the voltage from 12 volts to the laptop as most laptops will require slightly higher than 12 volts so you do have a power supply between the battery and laptop that should sort out any spikes. Have a look at the power supply that you have now,ie the 240v supply, and it will have the output voltage written in the specs, match this up with the jaycar 12v supply and you are good to go. Or as above there are automatic jobbies.
As others have said, I have been charging iphones and ipads etc for years out of a 12v car charger and no problem.
Cheers
Mike