Welcome to SR and I am glad you are deciding to get sober. You will find plenty of support and tons of info.
I do have some thoughts.
1. Yes, you can do this!!!! Sobriety is amazing and each day it gets better.
2. You need to get sober for yourself and if not then you will continue to battle the beast. I know because I did that on and off with my ex. We got divorced (thankfully) and I focused on myself and starting over. I am now in recovery. To stay sober this time.....I did it for me, by me and reached for all the help I felt I needed. I will never stop needing support and it helps me to give it!!
3. I don't know if that relationship can be salvaged. Not sure what drove you to drink while watching a 9 month old but I would say that chapter is more then likely over. That is my gut read on it.
4. Regardless, you need to give yourself plenty of time to begin working the steps of AA. Others here have far more knowledge then I do as I don't do AA and they are wonderful supporters and will help guide you.
5. There is 100% hope that you will get sober, stay sober and start your life over. To get sober you need to work on you.
Glad you are with us and looking forward to reading your journey. AA is an awesome program.
All the best!