Water storage: If the apartment has a dedicated water heater you will have its contents, typically twenty to thirty gallons, on hand. The toilet tank is another source, typically five gallons. Assuming there is some warning so you have time to store water you can store what you need. There are purpose-made plastic bags that can be laid down in the tub or shower and filed to store even more. A large garbage bag, would do much the same thing. Make sure the bag isn't one that is perfumed.

Getting to it: Drawing water off a water heater or filling a bag is much easier if you have a hose set up for the job. A six foot length of garden hose is fine and the drain tap on the water heater should fit the standard female hose end. Filling a bag is easiest if you unscrew the aerator from the sink or shower head from the shower and connect up the hose. You will need to have fittings on hand to make the connections. The guy at the plumbing department of the hardware store can fix you up with what you need. The connections are all standard sizes. These parts are available in inexpensive plastic that work well. While your there get a small pair of pump pliers, 6" or 7" will do, to remove the head or aerator and snug up the connections.

I would invest in a simple flat-bar type pry bar. A 16" or 18" model, about $10, could come in handy. In an earthquake the building can shift and jam doors shut. With a flat-bar you can lever any doors or windows open and get to your gear or son and escape the building. Consider getting a couple so you have one on the side of the wall you end up on.

Flat-bar types are particularly effective because they are thin and once inserted can be rotated laterally to multiply your effort. Being cheap is good also. They are also handy for many other survival uses, like digging through mixed rubble. IMHO no urban survival kit is complete without one.

I would check into apartment insurance. Without it if the place burns your out everything. Also make sure all your important papers are in one spot and ready to go. A sturdy waterproof container is good.