I'm another who has cats. I suppose I do 'mother' them, I call myself 'mummy' when I talk to them (although I know that's hugely disparaged on Mumsnet).
OP, a lot of people who have cats jokingly talk about 'the cat distribution system' but there is some truth in it - the right cat(s) for you come into your life at the right time - you find one another.
I was 24 when I got my first cat. At 18 it wouldn't have worked because I was off to university. I would say 18 is a little young to tie yourself to the commitment of an animal - a cat can live to 20 years or more, although obviously there are plenty of older cats looking for loving homes, you don't have to get a kitten.
Volunteering at a shelter might be nice for you if it's feasible, and would certainly stand you in excellent stead to look after a cat of your own when the time is right.
The 'hole' in your life that you described wouldn't necessarily be filled by an animal, or even children were you to decide to have them - it can be hard to diagnose the source of such 'holes' until you fill them but they usually point to a need for fulfilment in some way. That isn't automatically a need to nurture or mother - it could be a more general need to do something 'worthwhile' and might be filled by such things as a fulfilling job, gaining a qualification, finding a hobby you can throw yourself into, finding friends you really gel with.
18 is very young, don't feel you are lacking because you haven't quite found your niche in life. Follow your instincts and see where they take you. Your late teens and 20s are very much about exploring the sort of life you want, and then your 30s are more about settling into it, although it's never too late to change your life if you want to.