Can the dasha (planetary period) affect the timing of having children?

Yes, in principle. The birth chart shows the underlying potential for childbirth, primarily through the 5th house, its lord, and any planets or aspects affecting it. The dasha, antardasha, and transits act as the triggers that determine when — or whether — that potential materializes. For finer detail, astrologers also examine the D-7 (Saptamsha) chart, which is used specifically for matters of progeny.