That's a strange thing to want to do in a script. You're going to have to use the horizontal offset of the current insertion point to work out where in the next line to move the insertion point.
For example, you might use these techniques:
myIP = app.selection[0];
if (myIP.hasOwnProperty("baseline") {
// we have a text selection
myNextLine = myIP.lines[0].insertionPoints[-1].lines[0];
myHO = myIP.horizontalOffset;
nextHOs = myNextLine.insertionPoints.everyItem().horizontalOffset;
for (var j = 0; nextHOs.length > j; j++) {
if (nextHOs > myHO) {break}
}
app.select(myNextLine.insertionPoints);
}
I'm 3,000 miles away from my InDesign installations at the moment so I can't test that, but it'll sort of work. It the next line is on the next page, you'll be in trouble, and if there's a text wrap or something, you might end up at the start of the line after next. But this should give you the idea, assuming, that is, that you want to use JavaScript.
Dave