You can help by providing your daughter with an old calendar, and have her mark off the rest days explicitly, until she first bumps into Sunday. That is a perfectly legitimate solution. If the work needs to be handed in, the calendar with the marked off rest days is a complete mathematical proof. Then one might want to explore the markings to see whether there is structure there that makes it possible to reach the answer more quickly. The point of the above approach is that your student will be in concrete control every step of the way, she will know precisely what's going on.
Perhaps better, from the point of view of learning, is for the student to produce her own calendar. It may be a good idea to label the days $1$, $2$, $3$, $\dots$, $30$, $31$, $32$, and so on, so that numerical patterns in the marked off days can be more readily detected. But this is certainly not necessary.
The following is a much more abstract version, which should only be done after the concrete manipulation with the calendar. Think of the first Sunday as Day $1$. Then the next Sunday is Day $8$, the one after that is Day $15$, then $22$, $29$, $36$, $43$, and so on.
Now make a list of the rest days. The first one, we are told, was on Day $1$. The next one is Day $6$, then Day $11$, then $16$, then $21$, and so on. Continue until we bump into a Sunday. It will be soon: if we continue the rest days, we get $26$, $31$, $36$, got it!