I'd go for the rechargeables as well, for convenience and remote safety advantages. For the baby, maybe, but if nothing else I'd be tripping over the stupid cord.
If you do go with rechargeables, be careful about which one. Many D-cells are re-packaged AA's that cost more. If the mAh rating is 5000 or less for a D-cell then it's just a AA or C wrapped in a D case and will not provide much run time. Recent D-cell NiMh's supply 8000-12000mAh which should last nicely.
For comparison, high-end alkaline D-cells are rated ~12000-15000mAh.
Examples:
Eveready Energizer NiMh D-cell - 2500mAh
Eveready Energizer NiMh C-cell - 2500mAh
Eveready Energizer NiMh AA-cell - 1700, 2300, or 2500mAh
Eveready Energizer NiMh AAA-cell - 850mAh