My first date with my eventual 2nd wife (we met on line) had her bringing her daughter with her, which I thought was not the most responsible thing to do. We met at a restaurant, so it wasn't like zed and his Brazillian chick (still shaking my head at both of them), but still....
I was pretty experienced at the blind date/on-line thing by that time, but that was a first for me. She was kind of in the same situation you're in, though she had neighbors who were good friends and could have watched her daughter. I asked her afterwards if she thought it was a good idea to bring the kid seeing as she knew nothing about me. Her answer was "Sara has better instincts about people than I do". And I married her (the mom, not Sara).
I'm still not sure which of the last couple of sentences deserves the

emoji the most