Had the south won the war early and separated, I believe several things would have eventually occurred.

1. slavery would not have died out. I think it would have continued well into the early 20th century.

2. The USA (north) and the confederacy would have had further military conflicts because the confederacy was a near-fascist entity bent on expansion. Slavers already were looking at Cuba and Brazil to conquer and wanted to expand west. Westward expansion would have meant conflict over New Mexico and Arizona at least.

3. the Confederacy would have attacked and tried to take more of northern Mexico south of Texas

4. The southern economy would not have expanded and would eventually suffer from a loss of market for cotten due to the expansion of Flax Linen