Replying to Girls with kids

So how long after starting to date someone is it cool for them to introduce you to their kiddo? I just started hanging out with this chick and she's not the only girl I'm sleeping with and she brought her 9 year old daughter over with her the other night to stay the night and she actually slept in the same bed with us. She's hot and I like her and her kid was absolutely adorable but I can already tell she (the daughter) is already emotionally attached to me. I think I'm going to end up feeling like a piece of shit and breaking this little girls heart when all is said and done. P.S. her dad passed away in a car wreck a few years back. Should I just cut this off now? Any single moms out their that are willing to chime in would be greatly appreciated...