Employer Insurance vs State Insurance for pediatric specialists?

Hi, I just want to apologize for my wording before I begin and for any confusion it may cause, I’m completely ignorant on this subject.

Long story short, my girlfriend and I were talking about our future and the idea of marriage but she’s hesitant because if we get married, she’ll lose state insurance for her child but the number of specialists her daughter needs that takes state insurance seems incredibly limited. She keeps getting put on waiting lists and I don’t like that we have to wait over a year just to see a specialist for something that impacts her overall health.

I work for a hospital in New Jersey making roughly 85k/year and I don’t know anything about health insurance but I have heard multiple co-workers praising how great our employer provided health insurance is.

My question is: Am I missing something? I feel like it makes sense to get married and put her daughter on my health insurance plan so she can get access to a wider range of specialists that takes my insurance and hopefully avoid those God-forsaken +1 year waiting lists but both my girlfriend and I are completely ignorant in this area. Is there a benefit to state insurance that I’m not taking into account?