JavaScript queue implementation using linked list
Some observations in addition to the other answer:


inconsistent space between function name and () - use eslint or similar to prevent typos
Node is used as a template for extra properties, not as a type, so I doubt its name should be capitalized as though it's a class. Also, it's effectively unused in your code.
const in JS is not for named constants only, but for any value that's assigned just once:


  The reason is simple, it's much easier to reason about code when it is dead obvious what can change and what cannot change. [...]
  
  Going back and changing a const to a let is dead simple. And going const by default makes you think twice before doing so. And this is in many cases a good thing.
  
  How many bugs have you seen that involved variables changing unexpectedly? I'd guess a lot. I know that the majority of bugs that I see involve unexpected state changes. You won't get rid of all of these bugs by liberally using const, but you will get rid of a lot of them!


+ if you use a JavaScript IDE, it'll warn about accidental reassignment of a const identifier.
A separate assignment statement with newNode doesn't seem warranted as the code would be just as obvious with a direct assignment to head.
getSize is too verbose. I suggest exposing it as size just like the read-only size getter in Map and Set.
Since you're using ES2015, also use object literal shorthand: 

return {
  enqueue,
  dequeue,
  size: getSize
};