Reddit mentions of Sweet Sleep: Nighttime and Naptime Strategies for the Breastfeeding Family

Or you could just keep bed sharing. She'll eventually want to sleep in her own bed, all kids do.

I read Sweet Sleep which is put out by The Leche League. (https://www.amazon.com/Sweet-Sleep-Nighttime-Strategies-Breastfeeding/dp/0345518470/ref=mp_s_a_1_3?keywords=sweet+sleep&qid=1575144694&sr=8-3)
It makes some pretty compelling arguments for bedsharing and against sleep training.

We've been bedsharing since our daughter was 3 months old and its been a really positive experience. A lot of moms i talk to want to bedshare because it feels more natural and they like the connection of being closer to their baby overnight but feel guilty about it because they feel their baby "should" be able to sleep on their own already. She'll get there even if you bedshare now. Do what gets your family the most sleep and gives your heart the most peace. And check out the book for how to make bedsharing safe. Or read this article that explains how to make your bed safe https://www.llli.org/the-safe-sleep-seven/

If you are a breastfeeding family you should check out Sweet Sleep.
http://www.amazon.com/Sweet-Sleep-Nighttime-Strategies-Breastfeeding/dp/0345518470

If you don't want to buy it contact a local La Leche League Leader and see if you can borrow a copy. www.llli.org.

Do NOT swaddle WHILE bed-sharing. If you swaddle a baby you should put them in a crib or side-car style bassinet. If they are swaddled and anything obstructs their breathing they won't be able to help themselves. Happiest Baby methods are great for calming but once baby is asleep you can unswaddle.
Happiest baby video:
https://m.youtube.com/watch?v=guRi6zyFHtw

Bed sharing is extremely safe if you are prepared for it. With a baby this small you need a firm mattress and baby should be sleeping on the outside of mom (away from dad or other bed sharers) for a few weeks. Mom will naturally sleep side lying and create a safe space with her elbows and knees framing baby. If she normally sleeps belly or back she may benefit from a body pillow or regular pillow along her back to prop her up.

If you can, put your mattress on the floor. This eliminates the danger of falling. Once baby is mobile the room should be baby proofed and either gated or with a closed door. This allows mom and dad to continue to sleep and baby could move around the room and entertain himself safely.

OP, also remember that babies as small as yours need help regulating their breathing and body temperature. That's why baby is so comfortable on your chest. Try taking sleeping shifts for a few days just to get over the exhaustion. Then you can work on sleeping at the same time again. Good luck!

This one is sooooo much better. http://www.amazon.com/Sweet-Sleep-Nighttime-Strategies-Breastfeeding/dp/0345518470

I work in maternal fetal health and there is some concern about some of Karps recommendations (like swaddling which can lead to overheating and immobilize baby -- both of which increase SIDS). This is the one I recommend for my patients.

Seconded, you might want to look into the Safe Sleep Seven and the Book Sweet Sleep for some best practices.

https://www.amazon.com/Sweet-Sleep-Nighttime-Strategies-Breastfeeding/dp/0345518470 This book by le leche league had all the answers for me, except how to keep my arms and torso warm. I can't sleep with a shirt because then it's too hard for baby to nurse without us both waking up and I worry about suffocating him on accident, so I'm only wearing underwear and it's really cold! I also have to keep the blanket basically near his feet or he overheats. I'd also say that cosleeping is not very comfortable, I don't sleep as deeply as I did before baby because I'm always aware of his presence, I wake up every time his breathing changes or he wiggles. On the other hand it gives me peace of mind since I am pretty sure I would wake up if anything happened to him

Hey! It seems like you know what you're talking about... How do you combat books like https://www.amazon.com/dp/0345518470/ (Sweet Sleep) that say CIO is bad for brain development and has long term negative consequences? Ever since reading that book, my wife is ANTI-CIO and as such, we're hardcore bed sharing / attachment parents now... which kinda sucks but the kiddo loves it and we get plenty of sleep.... But HE has to be attached to us to sleep, forever now.

check out the book Sweet Sleep