Yes, it's true that in the past coins remained in circulation a long time, so that you could use one with Victoria's head right up to their withdrawal on decimalisation. This was possible because the specification of each value coin changed very little over the years.
However, since decimalisation, there has been a greater readiness to withdraw old and issue new versions of coins (the 5p and 10p pieces were replaced early 90s and there are suggestions that another replacement is on its way). My guess is that the Royal Mint will start to issue coins bearing Charles' head to the current specification soon after he becomes King (I'm sure they have planned for this) but older coins of QE II will remain legal tender. If a new version of a particular coin is planned, they will probably wait and issue Charles coins in due course, withdrawing the QE II equivalents.
It is possible that the arrival of a new monarch may prompt the Mint / Government to abolish the 1p and 2p coins, which now have little value.
I guess that it is much easier to introduce new versions of stamps, so we would see Charles on these very quickly. Again, the Royal Mail will have some plans already.