I'm another that really needs alone time.
My DH works away, permanently. I haven't seen him for weeks. So I am really really vigilant with bed times so that I do get to do absolutely nothing and be by myself. Other than that. No. The baby still sleeps with me. She's older and more independent than your bub though.
I try to get away by myself once a year for a couple of days. My girlfriends all offer to make it a girls weekend away, but in truth I don't want that.
I do have great mates though. Ones who just know when you aren't doing so well and offer to take a kid (or 3) so I can do the groceries.
There are weeks though when i feel exactly like you. The baby is up half the night so does have a day sleep, but I'm wrecked so i can't physically do anything, then she won't go to bed at night. That usually forms a pattern for a few days and I feel like there's no end in sight.