AITA for leaving my toddler with my 'childfree' sister for a few minutes, resulting in a trip to the emergency room?

I (18f) have a 2 year old daughter who lives with me and her father (18m), but spends two daytimes a week with my mom so that I can run errands (such as going to the doctors, doing the food shopping, cleaning the house, etc) and because my mom loves to spend time with my daughter.

My 27 year old sister was visiting my mom's house for the week from out of town. My sister and I have never really got on, when I got pregnant she thought it was the worst thing ever, and insists that children ruin your life and thinks I force my daughter on my mom (despite my mom saying otherwise). So, when I went to drop my daughter off with my mother at around 11am like usual, I was shocked to find my sister there alone. I asked her where my mom was, and she said my mother had gone to the shop and would be home within a few minutes.

My sister has always been very dismissive of me, she hates talking to me and will do anything to shorten the conversation, which is why I think this happened. I huffed because I was catching the bus into town to go the doctors, and it left in a few minutes. My sister rolled her eyes. I asked her if there's any way she would have my daughter for a few minutes just until mom came back, she had just woken up from a nap (she always sleeps in her stroller) so she would be happy to just sit on the sofa and watch TV until mom came back. My sister said 'absolutely not, I hate children and I don't feel comfortable being alone with her'.

Now, I completely understood this and I think she was very clear in saying she didn't want to. I called mom on the doorstep and she said she was just leaving the store now, so she would be max five minutes. My sister rolled her eyes and said 'Fine, I'll take her', and she took the baby out of the stroller. I was in a rush and thought my sister would be able to cope for five minutes. I didn't even think it would be a matter of 'coping' because it was such a short amount of time and the kid was tired.

So I left, and went for the bus. Literally five minutes later I get a call from my mom that they're taking my kid to the ER because she cracked her head open on the living room table. Apparently my sister had left the room for a couple minutes and my daughter wondered where she was going as she is never alone, so she tried to get off the sofa to follow her, and she slipped and whacked her head.

I am absolutely raging at my sister. I don't get how she could be so fucking stupid to leave a kid alone. She argues that I 'emotionally manipulated' her into babysitting, which I feel I didn't. She says she thought it would be fine to leave the kid while she made a cup of coffee, but I feel like it's common fucking sense not to leave a kid on their own for more than like two seconds.

AITA?