How do I date a single parent?

My girlfriend is a single parent. Her daughter is about 4 years old. We've only been seeing each other for about 2 months and I've never met her daughter yet. I honestly don't have a problem with meeting the kid but I don't know how to have a kid with a dating relationship. I've never dated a mom.
I won't lie, so far it's kinda hard. Her and I hardly see each other (maybe 5 hours per week or two) but we text constantly.
She speaks to me like it's entirely my responsibility to arrange how her and I meet. I feel that since it's her kid and I'm her boyfriend, she needs to arrange when and where. She's the link between her kid and I, so she should be the one responsible for making that decision.
I think it's a bit early in our relationship to be making any judgments if it's worth putting my 100% into. Dating a mom is really draining. If nobody is there to watch her kid while her and I are together our plans are cancelled. I can respect that though, she's a good mom. If her and I go the distance and end up having kids, her child might be a responsible older sister. Another hand for helping to raise my kids (if I even have kids).
Anyway, dating a mom is an entirely new concept of dating of which I'm not exactly sure how to handle 'the right way'. If any of you have dated a single parent, please chime in and leave some advise you wish you had while you were first dating. It'd be appreciated.

Thanks in advance.
How do I date a single parent?
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