You might still hear from her tonight, depending on how late she works, but I think it's a stretch to expect a same day response. Some will do that, others not, but it's not necessarily a reflection on the quality of their work. That said, if her response time grates on you, either be prepared to deal with it or find another therapist to interview because it's not likely to change.

As for what could happen in terms of scheduling in the future, maybe you could either schedule far in advance or ask for the same time/day each week.

But for now, you probably need to go in with an open enough mind to see if you like her.