Wow! I really love the dolphins!
I agree. The white doesn't really do anything. There are a few options I'd consider depending on your goal:
1) Grey sashing. This would create a very tranquil, muted look that would recede compared to the blue. I would probably quilt grey sashing in grey so the dolphins get more attention.
2) Pick something that matches that turquoise/robin's egg blue in your batik & use that. It will give it a consistent ocean look. Maybe try quilting that with a 40wt white thread with little waves or such.
3) Lime green. Analogous colorway. This would make a strong frame for your dolphins. I would definitely only quilt with a matching thread, if at all, as the color is already very strong on its own. Would really make for a playful, colorful quilt.
4) Fiery red-orange. Complementary color. Honestly, I probably wouldn't do the whole thing in red-orange, but maybe if you wanted to spice up the grey a bit, you could add red-orange cornerstones to add a bit of pop.
And actually, I'm not entirely convinced that bright white is out of the question. The texture of the white fabric you chose is competing with the texture of the batik. Picking a solid bright white Kona solid might actually look okay ... and if it needs to be toned down, you could always add some wavy lines in different shades of blue to break it up a bit.
I'm also thinking that if your dolphin block on point, that might add more visual interest. Plus, quilting around the dolphins in a matching blue (or as close to matching as you can get with a batik) would help the dolphins stand out more ... or maybe even consider a faux trapunto treatment on the dolphins to give them a bit of dimension. They just really blend it a lot at the moment.
Happy quilting!