My advice would be to get all of the to-do list started as soon as possible, as some of it can take a while to get sorted, your SC being one.
With regards to the vaccinations, these will certainly be valid for March 2020 and beyond. Yellow Fever is now life long. Diphtheria/Tetanus/Polio 10 years +, Typhoid at least 10 years with boosters recommended every 3 years. MMR requires a further dose 1 month apart to begin with and Meningitis good for 3 - 5 years. If in doubt speak/ask your GP and explain what they're for.
You're better off having them now just in case you do end up in the September intake rather than getting told you're in and not being able to join due to not having your vaccinations sorted.