Share your messagebase for other systems on your LAN

Install TB on your laptop
Tell it that you want to create a new account
TB will ask you for your mail directory, point it to the mail directory of your desktop.
Now you'll have to enter the name of a new account, give it the same name as it has on your desktop, this will make TB use those config files.
Repeat this for all of your accounts.

Apart from this you can pick two choices, either you use both setups as stand alone, this means that there's only one running at the same time.

Or you use one (preferrably at your desktop, since that's the existing one) as 'server' so that that takes care of the sending and receiving while your laptop has TB installed as workstation without TCP/IP.
The latter means that you'll have to change your desktop into 'dial-out server or TCP/IP', but that can be done at Options -> Network Admin at ny time without problems.
This has as advantage that you can keep TB running on your desktop without any problems, so your mail is being collected even when you're not behind your desktop and your laptop isn't running.