can I download operating system from a computer to another using Target disk mode

My Girlfriend's computer started moving slow and when you try to restart it it takes 30 minutes to load.. I tried to update the OS from the computer it's self but it keeps stoping in the end.. I was wondering is it possible to use my Macbook Pro and place hers into target disk mode and load the new operating system to her computer? and help would be greatly appreciated

thanks

Kelvin