Just seen your bumped thread.
I've no experience of the route you're planning, but my daughter and I travelled London to Istanbul and back in 1997. She on the back of my Ducati 900SS, aged 18. (Not a lot of room - no camping gear).
Our return route was Istanbul to Greece (Thessalonika and Corfu), ferry to Venice and home from there. It only took about a week, so 2 to 3 weeks should allow for plenty of diversions on your route. Our total round trip was 24 days.
(The route there was London, Vienna, Budapest, Romania (Sovata, Bucharest), Bulgaria, Turkey).
She liked the pillion on the Ducati, having accompanied me London - Moscow return the previous year, also in 3 weeks. A year or so later she got her own license and bike and set off further afield.
You don't say if this is your first long trip with your daughter - if it is, I posted an entry in another thread about the BIG difficulty (in my experience) of the first trip with your daughter - luggage.
Have a great trip!