First of all, are you using Auto Mode? Auto Mode will sometimes automatically pop up the flash. Try using Program mode or even Manual Mode. Then you can control when the flash goes off. If it pops up, just shut it again. Make sure your exposure is correct for the lighting.
There is a setting in the Auto Mode for no flash. If I were to take this photo - I would also use my 50mm 1.8 and and probably have it open all the way to 1.8 lol. I do also shoot in manual though. Worse comes to worse...I would underexpose it a little and just tweak it in photoshop w/blending modes or actions later.
IMO, under-exposing is better that over-exposing because it's easier to correct/edit afterwards. I take a lot of low-light photos and then tweak them with the 'curves' options.
Taking indoor pictures, esp. in the night/evening, is really tricky. Lots of experiments and practice! When all else fails it helps to accept the fact that life isn't perfect and neither are some of our photos, lol!