Hi Madeleine,
I'd completely forgotten about this thread, but yep I did do it. Don't think I took the Via Claudia in the end though.
From Munich I headed South along the Isar towards Bad Tolz, decent cycle path along a lovely river. I think there was a campsite in Bad Tolz but I continued along the river up to Sylvesteinsee and then Achensee, staying in a campsite right on the shore of Achensee for my first night. Lovely spot to camp (aside from an all-night thunderstorm) but it was quite expensive I recall.
Then went down into the valley and across to Innsbruck - I remember looking up a campsite in Natters near Innsbruck, but decided to go on and climb the Brenner pass before setting up camp on a patch of grass by the path just across the border into Italy.
From there I pretty much followed the cycle path by the Adige all the way to Verona through Brixen, Bolzano and Trento, camping one night in a vineyard on the way (not recommended with the kids!). Had planned on making a detour via Lake Garda (probably a few campsites around there) but sadly missed the turning before it was too late.
Let me know if you want any more details on the route, I can probably dig out the GPS log somewhere.