Yep, totally possible and pretty painless too . . .
You will need a IDE to USB device, can be found on the well known auction site for around £10-12 delivered if you are in a right now sort of rush then Maplin should be able to help.
Basically you are looking to connect a 3.5" IDE (PATA) Hard drive to the USB port of a computer.
Then connect to MacBook with the power supply connected to the old eMac HD and the old HD should just appear
You can then copy your files over to the MacBook, I would suggest you have a look on the Apple support website as it details everything there that you may want to restore i.e. Email, Keychains etc... that would save you hours of time.
Another option is to use the Migration Assistant tool to restore all of your data/settings/accounts from the eMac HD just connect the HD as above then launch the Migration Assistant ;-)
R