However, as she gets older I am concerned that laughing when she cries is going to be a bad reaction to have. No one likes being laughed at and I don't want her to feel like I don't care about her. I also feel awful about finding it funny in the first place, but can't help it.
I agree with the other answer that right now, she very likely cannot identify your laughter as hurtful behavior, but I think you're correct to be concerned.
Not all children are created equally, and not all people, be they toddlers or adults, will have the same response to being laughed at. There are "highly sensitive children", there are loud and confident extroverts, and everything in between. What kind of child you have depends on the temperament they were born with (though the difference between temperament and personality - and other factors - continues to be debated in the literature.)
One thing is pretty clear, though, and that attachment - the safety, security, and trust a child feels in their relationship with their parent - is dependent on the quality of their interactions early on.
I read that
laughter occurs after conditions of heightened tension or arousal when at the same time there is a judgment that the situation is safe or inconsequential.
So, your laughter is in keeping with this. However, in the foreseeable future, your baby/toddler may not perceive the same lack threat or significance, and laughing when the baby cries will affect attachment.
An example of this was given in a recent question:
My kid wanted to play, but as there were many unknown faces he roamed around holding my finger... He danced to his favorite songs and played, but all the while with me or his mother nearby. Suddenly he mistook my friend for me, and holding his finger started to dance and play. ...Soon he saw me in front and realized that he was holding someone else's hand. Everyone burst into laughter (including me), but he started crying.
The problem here is that the toddler perceived he was suddenly unsafe, while the parent knew otherwise. The parent laughed, the toddler cried.
Is it bad that I find it funny?
No, it's understandable.
How do I deal with the urge to laugh so I don't hurt her feelings when she's older?
Babies are not born "blank slates". Read about temperament, observe your baby/toddler, and learn what kind of baby you have. That will help you decide on what responses are best.
When your baby/toddler is crying, immediately try to put yourself in their shoes. Ask yourself what's funny about being hungry, fearful, tired, uncomfortable, etc. If there truly isn't anything funny about the situation, a stronger sense of empathy (which may well develop on its own with time, especially if this is your first child) should help you to respond appropriately, i.e. sympathetically.
N.B. For any who think this answer is teaching the child that crying about everything is encouraged by this approach, it's not. This is an approach to babies and young children that builds trust.
One of my children was extremely sensitive to being laughed at, even when they had done something incredibly cute and funny (in fact, the finger holding amid strangers thing referred to above happened to my toddler as well.) No amount of explaining that we weren't laughing at them made any difference. It turned out that we had a fairly sensitive toddler on our hands, someone who experienced the world very differently from us, and learning this helped us to adjust our responses accordingly.
Temperament and Its Role in Developmental Psychopathology
Autonomy in Adolescent Development, Towards Conceptual Clarity Edited by Bart Soenens, Maarten Vansteenkiste, Stijn Van Petegem
© 2018 – Psychology Press
Laughter in young children.