Why don't you just see how you go without one first? Then if you think you need one, then buy one then. It doesn't take long to go to the shops, buy a carseat and install it. Just do your investigating now (ie. investigate which carseat you may want if you decide to get one) so then you only have to go to the shops and buy it.

I admire you to be able to do so many things without a car. And for what it is worth, it can be done without a car. Our mothers and grandmothers etc did it. We (yes including myself) have just become lazy!

Good Luck