Most of us here also live near sea level, so experiences are similar. Since this is such a big trip for you, you should acclimatize like crazy, so you are ready. Bob's advice about sleeping high is important. I use Horseshoe Meadows, at 10,000 elevation.

Here's my favorite acclimation location: Trail Peak: Warmup / acclimatization hike

I'd definitely try to get to White Mountain -- early in your trip, maybe, so you can do easier hikes closer to Whitney. It is such a contrast to the Sierra, so you will be getting another great experience. If you don't make the entire hike, you could just visit the Bristlecone Pine forest areas, since they are all above 10,000.