RD,
If your combined estates are valued in excess of $3.5 million, you'll need to take advantage of a qualified domestic trust to hold the assets of the first to die in order to qualify for the unlimited marital deduction. If your combines estates are less than $3.5 million (or whatever the unified credit will be in any particular year), then whether you have a living trust or a simple will should not be affected by the fact that you're not U.S. citizens. Of course, there may be issues regarding any property residing in India and you should be aware of any tax treaties between the U.S. and India, especially if you anticipate any inheritances from relatives in India. Without looking it up, I would guess that the U.S. and India have a favorable tax treaty.
It seems, however, that your concern should be to insure that your property passes to the survivor and then to your daughter. If your daughter is young (I'd say under 25), then I would suggest a trust for any property she might receive before age 25. You can do that either through a living trust or a testamentary trust.
But, by all means talk with a local attorney and get this taken care of. You need to protect your daughter in the event of your simultaneous deaths.
Hope this helps. Let me know if you have further questions.