There are a lot of liquid investments that pay more than savings accounts. They may not be FDIC insured, but they are still pretty safe. For instance, my father insisted that all his money be in municipal bond funds. (He hated taxes, even though he didn’t make enough interest for it to be an issue.) His account was almost untouched by the crash, and it is still easy to get money out. It wouldn’t be good as a checking account, but plenty good for your needs. I’m definitely not saying that this is good for you, but there are plenty of options.
You don’t have to keep the money in relatively risky investments up to the time her first tuition bill comes due. You can start moving money to safer places before. We’re moving some money from more risky investments to ones that are more stable but are targeted to produce income as I get closer to retirement. But I do agree that you don’t want to be too aggressive, especially not when she hits 14 or so.
A diversified portfolio should have some bonds also. You can do better than `1%, but their value fluctuates also.