i grew up in india and have returned many times so my experience of india is not so much from the tourist or visitor's perspective.
You live in jakarta, so india will not hold that many surprises for you. northern and north western india is very different than say southern india. i would say for a first trip plan your visit carefully. tour group prices are of course way more expensive per day that those of us that have travel experience in india and can grab a train and navigate the stations, taxis and culture, but it can be very confusing to hoof it as a newbie. still with the right attitude, patience and confidence travelers still do it all the time.
india is not dangerous if you stay out of danger, that is do dumb things. getting scammed is the biggest problem, like let me get your rail tickets for you, first class sleeper...and you find you've paid 3X the ticket price, or take this taxi [you get the long way around town]. these things still happen to me and in the end i tend to laugh it off rather than getting angry.
the best of plans go awry, a 4 hour trian trip takes 16. be patient.
learn food rules, what to eat and what not to eat and stick to it religiously. i have gone without eating because i could not find food that was not risky. i always carry packaged snacks for instance and fruit that can be easily peeled. it is not true as someone suggested that vegetarian food is safer, nor food in the hotels. i've seen vegetarians get as sick as anyone, same for upper class hotel residents, it all depends on what you order. i have yet to get stomach/digestive ailments in all my trips...even still one of these days it is bound to happen. travel with cipro the wide spectrum antibiotic. i do eat heartily in india, it is important because travel there can be strenuous. travel light. if you are with a tour group though, they will lug your bag around, if not you will notice the difference between a 20 pound bag and a light backpack [one with the little wheels are a godsend].
tip well in hotels, the maid, the desk clerk etc. it goes a very long way to be generous if there are problems. i once sent my levi jeans out to the laundry from a 2 star hotel and got indian knock off jeans back. the desk clerk took up my case and the next day my levis were back even though i had left the hotel.
unaccompanied women traveling alone are safe, though they can be victims of grabbing, lewd remarks, suggestive behavior. women's sanitary facilities are not often much to the liking of western ladies. i have spent time with lone women travelers and their stories have not been much different than mine.
i love india so i encourage you to go. india always surprises me after all these year [since 1956] best of luck.