If you want a prediction of human behavior, fine. I suspect that we will move to a mixture of fusion, wind, and solar power long before our supply’s of fissile materials become an issue. I also expect that our initial expansion into space will primarily involve exporting technology into space and collecting raw materials from space. However, initial space exploration is going to have minimal impact on life on earth with few material goods being sent back and forth. I also suspect that it’s going to take far longer than 1000 years before 1 billion people live outside the earths atmosphere.
Edit: The Americas where "discovered" 518 years ago and dispite being there for the taking and far more hospitable than space 200 million more people live in India than all of the Americas put together.
Conceder: Between 1980 and 2006, the worldwide annual growth rate was 2%. (http://en.wikipedia.org/wiki/World_energy_resources_and_cons...) If you assume world energy usage will grow 2% per year for the next thousand years you end up with 400,000 times current energy usage however, the sun only supplies the earth with ~10,000 times our current energy use so we would fry the planet with waste heat far before that level. (Think global warming to 800 degrees Fahrenheit.)
PS: In 2009, world energy consumption decreased for the first time in 30 years (-1.1%) or 130Mtoe, as a result of the financial and economic crisis (GDP drop by 0.6% in 2009) so growth is not necessarily even guaranteed.