If you have an Exchange mailbox, this isn't an issue. Just set up your
profile on that laptop.
If you have a POP3 account, you would have to move your PST, ensure you have
your mail account set to leave a copy on the server, and set up your account
on the laptop.
If you have a POP3 account it might be easier to check your mail using your
ISP's webmail feature.
If your laptop is going in for repair, make sure you have a good working
backup of Outlook, just in case:
http://www.howto-outlook.com/howto/backupandrestore.htm