No need for a custom binding, just use knockout’s keypress event(Knockout docs):
<input type="text"
data-bind="textInput : keyword,
event: {keypress: onEnter}" >
</input>
And your function:
that.onEnter = function(d,e){
e.keyCode === 13 && that.search();
return true;
};
JSFiddle example
EDIT: New binding from knockout(3.2.0) : textInput – obviates the need to have a valueUpdate binding.