Big difference between f/1.8 and f/3.5?

I'm considering buying a portrait lens for my Nikon camera. One of my lenses is a 18-55mm f/3.5 kit lens. It was free with my Nikon D5100, so I never bothered investing into another portrait lens. Although, recently I began taking pictures of family with the kit lens and as expected, struggles with light conditions indoors. I'd like to avoid using flash indoors because when I've used flash before, it overpowers everything and even if I adjust accordingly, I get unfavorable shadows. So I'd like to avoid that route.

So now I'm interested in purchasing a Nikkor 50mm f/1.8 lens. Will I see a large difference in camera opportunity potential?

And will this mount on my D5100, DX format?
http://www.amazon.com/...00005LEN4/

Added (1). Thank you so much! I would purchase the f/1.4, but I'm buying a 40mm Micro f/2.8 lens soon for outdoor macro. So I can't get too excited! Haha Thanks again to both of you!

Yes, the f/1.8 is two stops faster than a f/3.5, and would probably save the day. Just a reminder a stop is half or double the light. In this case its double the light. Using the f/1.8 lens will give you 4 times the light for same settings as the f/3.5. I shoot a lot indoors myself, and having fast glass like f/1.8 is a critical part of what I do. Now when you are in tough conditions like shooting indoors and are not using a flash, the 50mm f/1.8 will ease that some. Nikon actually makes a 50 f/1.4 and even a 50mm f/1.2, but they are real expensive, but they let even more light in. The f/1.8 lens is pretty cheap and that is cool.

It will mount on your camera just fine.

Yes there will be a huge difference with the 1.8.
Much shallower depth of field too, so you need to pay more attention to focus.
The built in flash is always bad, but not all flash is bad, a bounced hot-shoe flash produces very nice results around the home, and you can get very creative using radio triggers with it.
For now though, enjoy the 50mm

An f/1.8 lens will let in roughly four times as much light as your kit lens at f/3.5. You'll also find that the optical quality of a prime lens is usually far greater than that of a zoom lens. I think though that you may want to consider investing is a good flash unit too at some point, used properly flash isn't overpowering.

Regard the lens that you listed it will mount on your camera, but operation will be fully manual, meaning you have to set the aperture using the ring on the lens, and you will have to focus it manually. Shooting portraits with an aperture of f/1.8 gives you limited depth of field, so manual focusing pretty much becomes a must, if you want to keep everything from nose to ears in focus - auto focus just doesn't cut it!