The trend of having fewer children is mostly in developed countries, it does not describe the majority of the world's population. And the notion of the population eventually levellng off is just one projection of several; nobody can say they know for a fact that will happen (if they do, they are categorically lying).

And peak oil isn't some relic of past thinking. It is a fact that the amount of oil being used is unsustainable. Sure, the speed of depletion might have been overestimated, but depletion is the inevitability (unless usage itself drops off). It's not just some magic resource being quickly regenerated like in a video game.

The Earth's land is mostly empty space for a reason; much of it is either (a) uninhabitable, (b) would be extremely expensive to clear and inhabit, or (c) ecologically essential. And that's all beside the point, because the predominant trend in population movement is urbanization; people are getting closer together, as cities become the main engines of the economy, not spreading out and looking for empty land to settle.

And the hypothetical scenario you pose is unrealistically calm. Funding will be the least of anybody's problems, because in such a scenario of environmental devastation and extreme population density, you are likely to see something akin to World War 3 break out. Cram the world's population in Texas (or even the whole of North America), and watch them make Israel and Palestine look like Bert and Ernie.