Thunderbird (like Firefox) has a profile folder. If you copy that to another machine everything should be the same on that new machine. I have been doing this since probably 2009 and I make use of filters.
It's absurd that this function (filter import/export) hasn't been built into the application. Why should people have to scrounge around in user directories (after having to look up the appropriate location for whatever platforms they're using)?
Also, can you have global filters? I don't want filters per E-mail account.