It is a good question tho, because all currency would have to change, along with postage stamps and god knows what!
That is what I mean, as far as old stuff goes it is a must, your not allowed to have currency as her, as far as I read it it basically becomes redundant, of course in the real world it will get replaced but on her death it basically becomes worthless and in terms of when the King died as I read Parliament does a few things basically making it legal tender until changed and you have the whole change over you have to do in x amount of time. Stamps are not hard but again will be costly and royal mail is not exactly swimming in money.
commonwealth Countries can adopt to be a republic on the death of the current monarch.
I could not find much real info really only what happened when the last king died, you also got to consider it was a while ago and laws and things have changed so I am sure while there has been half things done as always they are going to be half assed and after the morning and then celebration of the new king when crowned the cock ups will happen.
I think it is a fair question because while the queen is only a figure head we still have many deep routed things in regard to her that HAVE to be changed and it stretches over to the commonwealth, Here in NZ the currency also would have to change so really that alone is a massive thing globally.
Charles would be one of the oldest if not oldest crowned king/queen of England and he has a year to plan and have the coronation or even more bizzare things happen
Note:
I am up at 3/4 AM as My ear has been bleeding and from ear ache and headache