We did exactly that route last year, albeit camping, but we may repeat with a 'van in a year or two.
If you are not in a hurry, go though Belgium to Lux and stay at Kockelscheuer to the south of the city, then into Germany and stop at Camping Tenda near Russelheim, and finally into Austria and the Brenner Highway into Italy. This will bring you down the east side of Garda. The only charge will be for the Brenner Highway, but beware you will need plenty of pull as it is quite steep in places.
When you have landed, leave the car at Descenzano station and go to Verona and Venice by train - Venice takes two hours and costs about a fiver each way.