How to take photos of my hamsters without flash?

My friend gave me a Nikon D3100 that he had for a bit. He lost the manual to it. That was fine by me, because I looked up how to use it online and got the hang of it pretty quickly and learned by taking photos etc and that's no problem. The problem is, my hamster gave birth awhile ago and I've been taking pictures of them day by day with the camera watching their growth & development. This is all fine and the photos look great, but I use flash when I take them. I'm afraid that when they finally open their eyes, which should be soon, that this will hurt them. The room I take the photos in is my bedroom where the cage also happens to be and it's very dark in here. When I take the photos I hold the hamster under a lamp and I have the fan lamp on as well and I STILL have to use flash. I tried turning the flash off but the photos look really dark. I don't want to have to go outside to take photos of them. ;_; Is there a way to take photos of them without flash whilst still having good photos?

If You Can Tone Your Flash, Then They Should Be Okay.

I guess if your photos are dark you have not read the part of your user manual that talks about using the cameras light meter to produce good exposures.

If you are shooting indoors, you will need to set the cameras ISO to 3200 and shoot at shutter speeds of at least 1/500ths second. If there's still not enough light, use a 500 watt work lamp. Remember to set the white balance to incandescent to match the lighting you are using