It all depends on your ability to drive long distances , some people could do it easily , but for others it would be a struggle...The routes through Germany are very good , with plenty of rest stops if you need them , and the roads from Szczecin to Gdansk are pretty good too.....Speaking for myself i would say it is possible to do it in a day without exhausting your self , but nothing is worth killing yourself for , if you feel tired just pull off the road , take a walk , have some coffee and take a nap....i reckon you can do it ok.....
I've been driving from Gdansk to Dusseldorf for years, all i can say is that the drive to Duss takes about 12 hours if you're driving on your own, it's allright in Germany but the drive from Szczecin to Gdansk is a bit of a mare.... takes ages, because there's hardly any motorways. I guess Duss is about 2 hrs away from Brussels.
As a comparison I drove from Dusseldorf to Manchester, UK and that was a piece of cake in comparison to getting from Gdansk to west Germany.
Also there's usually a traffic jam somewhere on the A2 in Germany, so prepare to have a long and tiring journey. It is definitely doable. I'm a 23 year old girl by the way :)