Hi Zoe,
opinions on this vary wildly and I think really it's up to you and whether you think your child is ready to make the change. Your friend's mum isn't remembering incorrectly, she will have been of a time when everyone used the old-fashioned terry nappies - and probably not brilliant washing machines - so nappies were a chore you wanted to be done with quickly. My mum had seven children and some of us are as little as 14 months apart, but there were never two of us in nappies at any one time as we all were potty trained between 12 months and 18 months, pretty much as soon as we could walk as I remember.
As disposable nappies came on the scene mums tended to leave their tots longer in nappies, as there was less impetus to make the switch so it's quite common for children of up to two years and even beyond to still be in nappies nowadays. Whether that's a good thing or not is another, probably unanswerable, question.
One school of thought holds that those potty trained very early (before 18months) may develop bed-wetting problems. All I can say in that in our test case of seven none of us did.
So, basically, do your own thing, whatever you think is right for you and your baby, but don't be surprised if older mums remember things being done differently.
Hope that sets your mind at rest.