One thing I haven't seen mentioned yet is anything about security checks...YES, the stroller will have to be checked in the security line without your child in it (though your child can be riding in it right up until you get to security, you just need take your kid out and remove their shoes, too, to go through security). If it's an umbrella stroller, it can go right through the xray machine with the rest of your carry-ons. If it's a larger stroller that won't fit through the machine, it'll likely need to be hand-checked by the security people, so make sure you build in enough time to get that done so you're not scrambling to make your flight and get your stroller gate-checked.
Good luck and have fun in CA!