You can do it!
It will probably take you a couple of days, but there are national “highways” that will take you down through Gabon (passing not far from Libreville – which would definitely be worth making the detour to see!) and all the way across the Republic of the Congo, passing very close to Dolisie (the third biggest city in the RC).
Unfortunately, unless you want to circumvent thousands of miles you will have to cross the Congo river by ferry, which, as davidvc mentioned, is quite the trip indeed!
Make sure all your papers are in order and be ready to tip some highway checkpoints if they start giving you trouble. 5,000 CFA (~$10 US) ought to do the trick. It can be an expensive drive!