Well for one thing, there's no such thing as 12x18 inches on the internet. All that matters is pixels.
I assume what you meant was 12x18 inches at the default (i think) photoshop setting of 72 pixels/inch? That would be 864x1296 pixels, which I think is pretty reasonable for online posting. That's about what I use (usually 800x1200 for native camera aspect ratio)
You certainly don't want to go above the size of an an decent normal monitor, which is something like 1920x1080, and often smaller. Because people are going to want to view your whole photo at once, not by scrolling, and the maximum resolution they can do that at is their monitor. So anything higher resolution than the monitors is wasteful of space AND unnecessarily opening yourself up to more profitable image piracy.
That's big enough to see the image. If they want bigger, they can pay for it, or contact you, IMO. There's not really any reason why the public needs larger as a whole, all it does it let them print your stuff from online for free in larger print sizes with decent quality, and doesn't help advertise your skills.
ALSO, you don't want the internet browser to resize your photos for you, because they can look weird and have rounding errors. So making them smaller than a monitor is good for that reason too.
So 1200x800 for portrait orientation is already a bit too much, but it's close enough not to really bother my brain with worrying about it. Although maybe I should, due to the rounding error/resizing issue.