Want to leave cheating husband, staying for baby

One enters into marriage with dreams of hoping to start a new journey with their partner that is filled with love and happiness. For a happy and successful marriage, both partners need to be equally invested to work towards it. With the foundation of the marriage itself, trust and commitment, not in place, this is certainly not why someone enters into a marriage. I can imagine your pain and agony.

Before moving on any further, ask yourself if you are willing at all to give a chance to this marriage or not. Also try to figure out if your husband is willing to do the same. If either of you are not willing then the choice is for you to make whether to stay in the relationship or to leave.

If you choose to leave, as difficult as the process might be, it would help for you to avail counselling services that will help you through the difficult journey such as adjustments to living alone, getting support, handling children in divorce, finances, considerations for legalities, etc.
It is only natural for you to be worried about how your daughter might be affected in the process, but remember, staying in an unhappy marriage also has its influence over the child.
You could try reading these articles that I am sharing with you that might help answer more questions on this issue:
https://www.askmile.com/blog/parent-your-child-while-divorce/
https://www.askmile.com/blog/twelve-reasons-why-children-of-divorced-parents-deal-with-love-differently/

If you are willing, then what you could do is to try and figure out what is making your partner be disloyal towards you. Some of the common reasons could be
not emotionally invested in the relationship/ lack of interest towards the partner,
work pressure/ tension/ emotional exhaustion/ sexual frustration
incompatible personalities,
early childhood experiences/ learned behaviour
compulsive behaviour/ personality such that it is prone towards being disloyal
unhappy in the marriage
loved someone else
partner's needs not being met in the marriage.

It would help for you to explore what your partner's reason(s) could be for not being invested in the marriage. You could then have a talk with your partner regarding the same and mutually come up with ways you could cater to these concerns.
Here are some more articles you might find helpful:
https://www.askmile.com/blog/is-he-cheating-on-me-signs-your-spouse-may-be-cheating-what-to-do/
https://www.askmile.com/blog/7-ways-rebuild-trust-relationship/
https://www.askmile.com/blog/recover-from-infidelity-in-marriage/

It would also help for you to have a close friend/family member to talk to about this. Speaking with someone who understands you can help you unload a lot of weight off your back.