UPDATED Cats: loss of one of a bonded pair & what to do next

We had the worst weekend. Sadie, one of our sweet two year old sister kitties, somehow fell off our second floor deck onto the driveway below and sustained devastating injuries (ruptured diaphragm and spinal cord injury resulting in no sensation or movement in her hind end). We didn't see it when it happened - I was in the kitchen that the deck is off of and DS had gone inside to go to the bathroom. He was gone for less than five minutes. She was lounging on the deck when he went in and was gone when he came back. He heard a meow coming from below and looked over the railing and saw her. We raced her to the emergency vet and while they were giving us the initial update after exam and x-rays, she stopped breathing. They did CPR but couldn't revive her. We're heartbroken and so are her sister, Millie, and our dog, Otto. They have both been agitated ever since and have been wandering from room to room, looking for her. Millie is letting out the saddest meows. (sorry for all the details but peas usually have a lot of questions, so I thought I'd front load that information)

When we lost our elderly cat a few years ago, we waited for quite a while to bring home Sadie and Millie. We just weren't ready. This time, I'm wondering what the right thing to do is. Millie has literally never been on her own - she and Sadie had spent every day of their lives together. They played and cuddled and were always together. I'm wondering if it's better to get a companion for her sooner than later. 

If anyone has any experience with losing one of a tightly bonded pair of cats and has any advice on what's best for the surviving cat going forward, I would love to hear it. We will get a second cat sooner or later - if making the decision based on us, we would wait a few months until the pain of her loss isn't quite so fresh. But if it would be better for Millie to have a friend sooner, we can absolutely do that. We are devastated to lose Sadie but also want to be sure we do right by Millie. 

UPDATE 6/11
After talking it over amongst ourselves, with our vet, and with some trusted folks with a ton of cat experience, we decided we're going to add a kitten to the family after we get back from vacation next week. We are certain it will be a good thing for Millie, though we fully expect it will take some time for everyone to get along. We've done plenty of introductions before and are familiar with how to go about it.

What DH & DS don't know is that when they get back (they will arrive home two days after me), our new pal will already be here. I am picking up a very sweet little kitten next Friday and can't wait. I'll share some photos once he's home.