Well done for your bravery! Seriously!
I admit to pure cowardice, myself. And it is cowardice, not the wagging finger of caution! I backpacked through India, Nepal, Thailand, China, Malaysia, Indonesia- you get the drift!- to Australia over 9 months at age 24-25. I had an absolute whale of a time but the idea of taking the DCs on a trip to India brings me out in a cold sweat, sorry! DH undertook a similar stylee trip to mine at the same age through South America for 3 months and is of the same opinion.
However, there's no doubt about it, we did it relatively cheaply, but not 'seat of the pants', but it did inevitably involve being jostled a lot, fighting to the front of queues, 4 hour bus journeys that took 10 hours, landing you in the middle of nowhere at 3 a.m., waking up in you train sleeper to find someone else's child laid across your feet etc! I wonder how much of that you can avoid (unless that's integral to your 'India Experience'!) by paying out more? I guess all levels of comfort are catered for.
My greatest fear for me, then, and my DCs now is getting sick in somewhere inaccessible. So I suppose the best 'advice' is that already given, about water, hand hygiene paying out more for better food etc!
Didn't that Irish author, De(r)vla Murphy write about her experiences of travelling through India with a child? Or am I thinking of someone else? She really did go 'on the cheap', sleeping on the roofs of ferries by night etc, I recall!
I hope all goes well for you as you will have the most fantastic and memorable trip if you do!