Just got back to UK from good old Corfu therefore taking oposite direction.
For driving Corfu - venice (or vici verci) is best option, Brindisi or Bari is further down than it looks (I've used both in past) and down there you'd better take your car wheels into the hotel at night.
My route briefly
Friday 7.00am greek time ferry to Venice arrive 9.00 Greek time (8am Italian time) Venice towards Milan, turn right just after Verona towards Brenner/Brennero (Brenner pass).
Brenner pass (and all other minor roads I tried to find) was closed for 4 or five hours when I got there so I joined all the skiers in their gear for a sing song , me in t-shirt, bit out of place.
Finally opened, went on way .... advice if you buy snow chains and there is a heavy blizzard blowing with ice on road in minus temperatures then use them... I couldn't be bothered hence missing nearside wing, indicator and bent bumper, landrover road tyres don't like ice either, I did three pretty full piruouettes smacked into central reservation and then slid into middle of motorway, low points for skill but quite high on artistic impression.
Another piece of advice, Italian toll booth collectors spot foriegners easily, you roll up to pay, hand them a note, they give you back small change and raise barrier and show green light, pressure of vehicles behind cause you to put foot down before you realise you haven't been given your small notes as change. If you do wait the collector has them in his/her hand and will give them to you, neat little trick, They've tried it three times on me now, the first time it worked.
Anyway continue to Innsbruck, you can turn left (A12) and find a slip road that leads to a minor road leading in turn to the A7 in Germany or turn right on the A12 then A8 to Munchen. For the former I would suggest you use one of the routeplanners and zoom in on this area to print it because it is easy to take wrong road, I know from previous xp, coasting round Austrian Alps at 1am is not good.
Head to Ulm then Stuttgart, KarlsruhePirmassens (zoom in and print this area too) Saarbrucken, into Luxenburg (buy petrol/diesel here, it's cheap). To Brussels (RO ring road, avoid rush hours, m25 type area), head for Gent then Ostende/Dunkerque. Use Norfoplk lines from Dunkerque to Dover they are keeping ahead of the competition.
Hope that helps a little.
PS I did it in 2 days almost non-stop up to Yorkshire in an old landrover with a leaky radiator (kept heating on full all time thermostat luckily stayed closed so lost no water) and , as has been said better to take rest stops, I chanced it but that was very stupid.