It really does get better, trust me. It doesn't seem like it right now because she is still so young, but you will get a handle on things. It may take several years, especially if you have more children, but it does get better.
Right now your expectations about how much you can accomplish around the house should be set reasonably. It's not realistic to have the house spotless and still spend the quality time with your daughter (which is the priority).
I felt just like you did, but realized that I couldn't get it all done. So, I picked the most important things...the items that helped me feel better. Aside for caring for my baby, I always made sure the kitchen was clean and the cat box was kept up. The laundry piled up, the furniture was dusty and I never mopped as often as I should, but the kitchen was clean. The rest I got to when I could, but having my expectations set reasonably helped me to not feel like a failure.
It also helped me to make a small list of things I needed to do. Again, make the list reasonable and include things like grocery shopping, story time at the library, emptying the dishwasher. It feels good to cross things off a list. I bet you are accomplishing much more during the day than you are giving yourself credit for.
And don't compare what you are accomplishing during the day with other moms...maybe they aren't spending much time with their baby, maybe they have help, and maybe they are as stressed as you are. You do what works for you and if that means no chores for a few days, then that's the way it is.
Hang in there...it really does get better.