I met a girl week before last on a Saturday in which I got spoke to her for a bit, got her number, and then texted her that Wednesday. Our response times were very sparse (a few hours in between each) in which I don't mind/care as I was busy during that time. At one point during the conversation, she didn't reply for a day or two in which she eventually does, apologizing, saying that she is sick and didn't feel like speaking to anyone, blah blah blah-- That was on Sunday (2 days ago) in which I haven't responded yet

The conversation between us has not been long in terms of text sent, but long in terms of duration. There was not really much of a "peak" in the conversation, but she has been responding well (lengthy responses, asking me questions, etc.). I plan on suggesting that she joins me on some activity I'm doing this weekend in which I wonder if it would be unwise to ask now as I didn't ask while the conversation was at its peak (there haven't been much of a peak). Also she may still be sick in which this weekend she may be returning back home from college or may not want to go out as she is sick. Would it be unwise to invite her out with me?

Are my thoughts rational or is that just my hamster spinning to not invite her out? I don't want to continue this conversation in text in which I want to invite her out in which if she joins me, reschedules or doesn't come, I will keep it moving.