Unfortunately, I've never seen an install of OE able to export mail.
The only solution I found was to search for the files, and copy them to the OE folder. If I remember correctly (its been awhile), the necessary dbx files are located in: "C:\documents and settings\YOUR_NAME\application data\idenities\microsoft\outlook express". There may be more folders in here with random numbers & letters if you have more than one account setup, and you'll have to manually figure out which directory is which.
Copy those files over to your laptop.
You will loose your filters, and your account settings. Those will need to be manually recreated. You should be able to export your address book.
I know you didnt ask about other applications, but you might want to check out thunderbird. It can import your current OE items (filters, addresses, mail, etc) and moving it to a machine is a cinch, especially if you get the mobile version. Regardless it also lets you choose where your mail items are stored, but by default its in a similar location in the idenities directory, but the difference is it also has your settings in there too.
OE is a pain when you need to move. I had to do the same as above. Right click on your Inbox and look at the properties and then the location of the file. Just copy the whole folder over to your new computer. Then setup all the accounts again.
Outlook is much better, glad I made the move over to it.