Is it bad that I don’t feel like I love my girlfriend of one month yet?

We had a small argument because of 2 things 1) she mentioned that she wanted to get a pet turtle for both of us. She wanted to take care of the pet for one week in her house and I would take care of the pet the next week in my house. When she mentioned this I said I didn't believe I was suited to take care of a pet turtle at the moment but she could get it for Boths of us and she could take care of the turtle. I say she could get it for both of us because she mentioned that this turtle would represent our love in some way. 2) My mother's birthday was today I was spending most of the time with her and took her to the mall. Sometime later that day she asked if I didn't want to see her because I hadn't mentioned anything about seeing her. She invited me to see her in a park and I agreed but then my brother mentioned that we were throwing a small family party at home for my mother before the big party on the weekend so I had to cancel on my girlfriend. I did make the mistake of taking 24 minutes to be exact to tell her I wasn't going to be able to make it to the park to hang out with some of her and some of her family members. She proceeds to tell me “I see it this way if you really care about somebody I will do anything that's on my hands so that they can feel good”.

Is it bad that I don’t feel like I love my girlfriend of one month yet?
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