A bunch of things you must remember....
1. You like the light in the room, but your eye is far more sensitve to light than the CCD in your camera. So what looks like enough light to you may not be enough for your camera.
2. In the viewfinder of the camera are little squares. If you are set to spot or center weighted metering, a different square is highlighted when you press the different directions on the control pad on the back of the camera. The camera uses this square to determine what you want to meter and focus upon. If you move the square to the edge or corner, the camera will meter for the corner of the image.
I bring this up because if the square is not on your subject, the camera will meter for whatever the square is upon. If your dog is center of the view finder, and the illuminated square is on the edge, your camera will make aperture priority determinations based on the edge of the image.
3. When you are using TTL (through the lens) metering, the camera is metering for 18% grey (a light grey color to us). However, the camera doesn't see color, it sees light intensity. So experiment.
4. Skip A and S settings. Go straight to M. Learn to shoot in manual mode, and you will learn how to use your camera.
5. Metering - put the square in your view finder on your subject and lightly depress the shutter release. There should be a little bar graph in the bottom of the view finder. Adjust aperture and shutter to get to a metered exposure. Later, you can build in an offset for metering if you find your camera meters a little light or a little dark (it does).
6. Speedlight - If you manage your white balance and flash bounce, you can get your speedlight photography to look like natural light. You need an external speedlight that can bounce off the ceiling, or a diffuser box, to avoid harsh shadows. The built-in speedlight on your camera will not work for this.
Lastly, to answer your question, you may need to increase the ISO setting. However, make sure you are metering the correct object in your view finder.
1999 e46 328i Ti Silver / Black[retired]
2007 e90 335xi Jet Black / Black[retired]
2011 e70 X5 35d Vermillion Red / Cinnamon
2011 e92 M3 LeMans / Fox Red extended