This example is assuming you're defining "next week" as "7-14 days in the future", but you could tweak this answer to do whatever you want. This answer is intended to help understand how to perform this sort of operation on javascript Dates, not just this operation specifically.
Option 1: Determine how many days are between the target date and the current date by subtracting the current date from the target date
// store current date as "today"
var today = new Date();
// store 8 days from today as "later"
later = new Date();
later.setDate(later.getDate() + 8);
// Determine how many days are between the two dates by subtracting "today" from "later" and converting milliseconds to days
days = (later - today) / (1000 * 3600 * 24);
// Is "later" 7-14 days away?
console.log(days > 7 && days < 14); // true
Option 2: Store the start and end date and compare those to our target date
// store 8 days from today as "later"
later = new Date();
later.setDate(later.getDate() + 8);
// Store the start date
start = new Date();
start.setDate(start.getDate() + 7);
// Store the end date
end = new Date();
end.setDate(end.getDate() + 14);
// is "later" between the start and end date?
console.log(later > start && later < end); // true