When working with dates in JavaScript, it's usually handy to use a library to do some of the hard work for you - e.g Moment.js: http://momentjs.com/
With moment.js, for your scenario you could start by creating a moment at the start of the year you want. Then add the number of weeks corresponding to the week you want. You can then loop through setting the day of the week (Sun, Mon, etc) and caching the date for each day of the week into a list as your loop progresses.
E.g:
var datesOfWeek = [];
var workingDate = moment(new Date(year, 1, 1));
workingDate.add('weeks', week);
for(var dayOfWeek = 0; dayOfWeek < 7; dayOfWeek++) {
workingDate.day(dayOfWeek);
datesOfWeek.push(workingDate.toDate());
}