Rhubarb, I think that at your daughter's age you would be fine, but if you're going to do it, do it soon. My ds is just 5, and for about certainly the last 12 months has had some very definite friends who he would miss very much if we upped sticks now. Plus, my experience of changing schools at a young age was very painful, and I found it hard to make friends (but this may depend on the child - I was shy and hopeless at sport).
At your dd's age you are her main stability, so provided you are constant she should adapt. Again, it probably depends on the child, but certainly we've never had any problems travelling with our two children (we've never done a long trip like you're suggesting, but our two seem to settle just about anywhere). Yes, there will be challenges in travelling with a toddler, and it won't be quite like the old backpacking days, but it will still be exciting.
As for your dd being too young to get anything out of it, who knows what sticks in little minds? And surely a happy and excited mum is going to have a positive effect on your dd? You'll see and do different things with a little one in tow, and in my experience a small child is a great icebreaker in many places.
Take a look at the Lonely Planet book 'Travel with children' for some practical tips on getting about and for inspiration. And when you go make sure you have access to e-mail somehow from time to time to let us know how you're getting on!