Welcome to Nikonians! You have a few options. The D5100 should produce a reasonably clean image up to about ISO 3200. ISO 3200 is a 1 1/3 stop difference compared to ISO 1200 which will allow you to use a shutter speed twice as fast as the one you were using and stop the aperture down 1/3rd stop. Always use the lowest ISO setting possible for the given subject and ambient conditions.
You can also set the ISO to Auto mode with the minimum shutter speed set to 1/60th or 1/80th sec. and the maximum ISO set at 3200.
Another option is to use the built in Speedlight. Depending on the situation, you will want to keep the ISO set to 800 or lower when using flash and the WB set to Auto or to flash if the flash will be providing well over two stops of the exposure or more. Good Luck and Enjoy your Nikons1