Hi there! You're going to have a great time. India is big fun.
Planning to stay the first week in Delhi and environs is a good idea. India can be incredibly hard on your senses at first and you need a few days to just chill out. The trip to Agra can easily be done in one day if you want, but I recommend staying a night so that you can spend more time at the Taj and see it in varying light. It's wonderful.
What part of Rajasthan are you planning to go to? For one week including fitting in a 3-day camel safari I would say no more than two cities max. Jaisalmer is the most popular camel safari stop although I've heard they can also be done from Bikaner. Bikaner has an advantage over Jaisalmer in that it's not NEARLY as hell-and-gone west, but it's also not as interesting a city. For your second Rajasthan stop I would HIGHLY recommend Udaipur. It's an incredibly beautiful fairytale city. Don't miss it!!
I don't know much about Gujarat other than I want to see the Rann of Kutch sometime. Sweet. Make sure to write about your experience!
If you're looking for quiet reflection at the end of your trip, well, I wouldn't recommend Goa. It's more of a beach party lifestyle there. If you want something a little more chilled out, head to the beaches of Kerala instead. You MUST see the backwaters-- in my opinion the best place to relax and "get away from it all" in the entire Indian Subcontinent. Seriously.
The only problem with Kerala is that it's about another 12-ish hours south on the train from Goa, so it'll take longer to get there... but it's SO worth it! Really! go go go there.
I have a bunch of pictures of India (and pertaining to what I've recommended, Delhi/Taj/Udaipur/Kerala as well) located
HERE.
Let us know what you decide!