I think the most fascinating part of the future of our planet to speculate on is the carrying capacity. At what point will our planet experience a catastrophe due to sheer populations numbers? Or more likely, when will a catastrophe be made much worse because of overpopulation? I'm pulling this figure off the back of my brain, but I want to say the predicted max world population in 2050 is 12 billion. How the hell are we going to support all these people? Existing programs in developed countries are already under stress, and developed countries are experiencing civil unrest due to large unemployed youth cohorts. I personally think a strict population control program along the lines of China is required to mitigate these problems, but they will never be enacted. Instead, the world will just be bogged down by an excess number of people and will settle around a miserable number of people. perhaps 9 or 10 billion.
It's been predicted that once we reach a certain point in time (e.g. 2050), human population will begin to decrease and eventually stabilize rather than continue to rise indefinitely. The reasoning is that as more and more people have access to education and thus middle class wealth and lifestyles (developing countries become 'developed'), the average birth rate will fall. This is already happening in many western countries, where immigration is the only thing keeping populations stable. If this is this case then a Chinese style population control program would be unnecessary. However, spreading education to many developing countries is easier said than done. The result: Bangladesh, as one example, suffers from extreme overpopulation and one of the highest average population densities in the world. This has already contributed to more disastrous catastrophes numerous times in the country. The '91 cyclone killed ~200,000 people because, among other reasons, there were (and still are) thousands of people packed into every square kilometre along the coast. Overpopulation will likely not reach an unsustainable level, but this doesn't negate the fact that it still causes certain problems now. Food for thought I guess.
What you're describing is stage 5 of the demographic transition model, where reproduction rates decline as the standard of living increases. There's actually some evidence of a stage 6, where reproduction rates start to increase again in some advanced countries (but not Japan).
I think the carrying capacity really depends on how the developed world lives in the future. Will we continue to use far more resources than our necessary on a daily basis, or will everything (food, water, electricity) be scaled back to more sustainable levels? If we continue on our current path, I agree with your prediction. If programs are enacted and consumption reduced, I could see upwards of 15 billion being somewhat comfortable.