Tracks that you buy from iTunes can be authorised for use on 5 computers. So if you buy them with your account you will need to authorise her computer too. That's easily done, you just double click the bought track in iTunes on the laptop and it'll ask for your account password. All tracks purchased by you will now work on that computer. You can sign in to the account on her laptop for buying music without any bother. All the bills will go to the card registered with the account.
I'm pretty sure the tracks will be ok on her ipod too but if you already have a bought track it might be worth trying it out before you buy more.