Workstostaysane, if you decide to carry on bfing and you are not comfortable with it being a public thing, you can negotiate with a toddler. I know some people who only breastfeed in private, or at bedtime, or whatever.
However if you're wondering if it will feel odd to you to be breastfeeding your older child, the answer is no, not really, it mostly feels completely normal, because each day, they are only a day older. If you had to start off feeding a 3 year old I think that would freak most of us out But as part of a continuing process the age of the child being fed doesn't really register - it's just "my child, who wants me to feed him / her".
As for nutrition, that's a bit of a red herring, I think. It's great to know that breastmilk passes on such health benefits for both mother and child but breastfeeding an older child is about soooo much more than nutrition. It has so many emotional benefits.
It's also the easiest and most pleasant way to calm a tired, tantrumming toddler - and it calms you down in the process, as well. I personally would do it again just for that reason alone!