Oh they didn't wait to the end of the war to make a consitution. They whipped theirs up in 1861 (effective in 1862) here it is. http://avalon.law.yale.edu/19th_century/csa_csa.asp

To answer your question about branches: Yes, they did intend to have the three branches. In fact, a lot of their consitution was copy and pasted from the USA consitution. (With the names and dates changed) you might say though, if they had a consitution why did they only intend for three branches and not actually have them? That's because the confederates never got around to setting up their supreme Court, a pretty important part of the judiciary.

The other two branches though existed and functioned throuout the war. The confederate Congress held two elections. There was no political parties in the same way we have parties. It was more of a pro-admin and anti-admin system. The confederate executive was made up of President Davis, obviously. He was assisted by a large cast of characters in his cabinet who often came and went throuout the war.

But basicly, their plan for after the war was to keep trucking along with more or less the same political system they were used to under the United States. The largest change in the confederate consitution from the USA was that it entrenched slavery into the consitution. Not only could the confederate goverment not ban slavery, state goverments couldn't either.