Did you know, that we have actually reached "Peak Child" and have been there for some years. As the other answers have said, then we do have enough resources if we use them well, as large parts of the world are under populated still.
You should watch this video if you haven't seen it yet:
There are some questions here - about the projections - mainly due to countries like Nigeria especially - has a high population, and still has large families and rapidly growing - but if they follow the same trend as everyone else then should be okay.
Most current projections are less than 10 billion for the peak population.
Theoretically, yes, we could move our population off the Earth. Not with existing technology - but if we get to the point where we can fly into space as easily as we can cross continents and oceans, then we have about a billion passenger flights a year - so, theoretically could move entire population in planes within a decade or two - in same way could move entire population in space planes if they become as economical as ordinary plane flights.
But there is nowhere in space for them to go to - that is - unless we make large space habitats that are easy to maintain. Because nowhere in space is anywhere like as easy to live in as the less populated areas of the Earth, e,g, "seawater greenhouses" in deserts - or "sea city" floating on the sea, or even floating in the atmosphere in a Buckminster Fuller type "cloud nine" tensegrity sphere - all of that is easier to build than habitats anywhere in space in our solar system outside of Earth.
Even a Stanford Torus in space (one of the easiest to build, and make comfortable for humans, and one of the easiest to maintain once built of the various ideas) is surely harder to build than a Cloud Nine tensegrity sphere floating in our atmosphere.
Same applies to a Venus cloud colony - Buckminster Fuller's "cloud nine" transferred to the Venus atmosphere - though that might, possibly, be easier to build than a Stanford Torus - at least, far less mass per colonist - it wouldn't be as easy to build as a "cloud nine" colony in the Earth's atmosphere.
So - has to be some other reason for going into space - certainly not just a way of escaping over population, can't see that working as it's far easier to build extra places to live, and use same technology to produce food etc in those habitats, on the Earth.