Routine checkup vs. suspected cavity: what should I do?

I’ve noticed this dark spot on my tooth—I have a nagging suspicion it might be a cavity—so I went ahead and booked an appointment with my dentist. However, I only requested a routine checkup and didn't mention my specific concern about potential decay, which resulted in me being scheduled for the end of the month. Would I have secured an earlier slot if I had been upfront about having a specific issue rather than just asking for a standard cleaning? Is it possible to request an expedited appointment by citing the suspected cavity?

Not at all. Waiting about a month for an appointment is perfectly reasonable. At my dentist's office here in the States, you usually have to wait four or five weeks just to get in the door. A cavity isn't an immediate crisis; it won't suddenly spiral out of control in three weeks.
You'd likely get seen much sooner if you were in actual pain or dealing with an infection. If things were inflamed, they’d squeeze you in today or tomorrow. But since you aren't hurting, you just have to wait...