Princess, I understand your pain and exhaustion, but it is more painful and demoralising trying to get an uninterested parent to pay attention to the wonderful kid that is growing in your home. It took me a few years to accept it, but both DS and I are much better since we have given up on dad being a "proper" dad. Some people call it stability. I call it peace of mind.
Be proud of yourself, you really need to be someone special to work and raise a kid on your own. Things are difficult now because your child is very young, but in a couple of years she will get interested in other things and will not need so much attention.
Sometimes you really feel the weight of so much responsibility and need a time off but if that doesn't materialise, you may just need to be creative to find it:
The most jmportant thing is to have a good sleep. If you are well rested your threshold of tolerance increases in a massive measure.
When DS was that age, I was working 30-35 hrs a week and the daily commute was taking almost 3 hrs. The way I survived was very simple:
Serve dinner around 6, do a quick tidy up of the kitchen, full attention to DD for one hour, bath and aim for both of you to be in bed by 8.
If you go to sleep so early, you will wake up very rested about 4 am. Blissfully quiet time of the day. I used to do half an hour of yoga, an hour of reading, tidy the house and get myself ready before DS woke up. It certainly made things not only bearable but very enjoyable.
Cut yourself some slack, you are doing great, you are just tired and need some rest.