I just got back from that exact trip yesterday. We spent the first night at chicken spring lake. I don't think we ran into any water until we hit Rock Creek, which has plenty.
Then you will go up a steep hike, just over a mile to Guyot Creek, which is a bit smaller than Rock Creek. After that, you won't run into any water until Whitney Creek (4 miles or so), which is in the Crabtree meadow area. You will follow this creek up a canyon for a mile or two. There will be a few spots to get water past Whitney Creek. Then you'll hit Timberline Lake, and a mile or so past that, Guitar lake.
Make sure you bring enough water with you when you leave Guitar lake, to go up a tough, tough climb to the Whitney Trailhead. There is no water from Guitar until you descend halfway to trail camp after you already conquer Whitney. Among the billion switchbacks on the Whitney portal trail, there is a spring that follows the trail for a bit, and you can filter water there. After that, there are plenty of places to get water on your way back to the portal.
We camped at Chicken Spring, Rock Creek, Guitar Lake, and then at Outpost camp on the way out. Great Trip!!!!!
Keep in mind that is is warm, and there is no shade in many places so you will need to stay hydrated.
