split.js

function split(string) {
  var curr
  , lastQuoteIndex = 0
  , lastSpaceIndex = 0
  , parts = []
  , isInQuotes = false;

  for (var i = 0; i < string.length; i++) {
    curr = string[i];
    
    if (curr === '"') {
      if (isInQuotes) {
        parts.push(string.substring(lastQuoteIndex + 1, i));
        isInQuotes = false;
        lastSpaceIndex = -1;
      } else {
        isInQuotes = true;
        lastQuoteIndex = i;
      }
    }
    
    if (/^\s$/.test(curr)) {
      if (!isInQuotes) {
        if (lastSpaceIndex === -1) {
          lastSpaceIndex = i;
        } else {
          parts.push(string.substring(lastSpaceIndex + 1, i));
          lastSpaceIndex = i;
        }
      }
    }
  }
  
  return parts;
}

console.log(split('"fish" boo biz "bar bax" qrt "zoo"'));