Not sure about the short-term, but in the long-run:
Von Braun's team probably keep designing rockets on a theoretical basis, and maybe get hired by the French or West Germany down the line for the early European program, if they don't immigrate to the US.
The Soviets probably build the R-7 series of ICBM more-or-less on-schedule, though the Scud might get butterflied (it was the most similar to the V-2 of the USSR's OTL arsenal). They still need a nuclear deterrent to counter the US's bomber force.
The US also develops missiles, though a couple of the OTL boosters won't exist, so other contracts will go out.
If I had to make a guess about the short-term, though, Hitler probably takes the money/fuel/aluminum that went into the OTL program and pisses it away on some other delusional fantasy about striking back at the British. Maybe V-3 cannons, or more Amerika Bomber prototypes.