I am very pessimistic about Nazi Science post war. While German scientists developed many brilliant innovations at the time, their next generation replacements would have learned a highly indoctrinated education designed to make them loyal, not innovative.
The Future of Nazi Science might well be scary wacktards like Mengele, not meaningful competition with the United States.
The Defense industry label and the importance of ICBMs can't be overstated, but this would be only the beginnings of a space program. The Nazis' technological edge over the USA will fade away as the indoctrination destroys scientific inquiry in favor of some kind of Nazi Lysenkoism.
What happens when Von Braun dies and his replacement knows jack crap about rockets other than Nazis invented them and half the other things of the world?