Whether you use a flash or not should be dictated by the level of available light. If enough light is available for photos to be taken at a reasonable iso (for your camera), then a flash won't be necessary. If a flash is necessary, then you will greatly benefit by using a modifier to redirect, diffuse or enlarge the light source. There are modifiers available for your on camera flash as well as external flashes.
ON Camera Pop-up Flash Modifiers:
One problem using the on camera flash is red-eye, the bouncing back of the light source from the blood vessels in the retina of the eye, giving them a glowing red color. Redirecting the flash will eliminate this. One example of this type of modifier is the
Lightscoop Universal Standard Mirror Bounce for Pop-Up Flash, 29.95 from B&H. It redirects the light to bounce off the ceiling from the ceiling. If you can't use the ceiling, i.e., too far overhead, painted black, etc., red eye can usually be be minimized by using the cameras red eye setting, which prefaces the main flash with a series of pre-flashes, this causes the subjects irises to close down, or it is usually easily corrected in post production.
However, if not re-directing the flash, you will still want to diffuse the flash to remove harshness and shadows.
A couple of diffusing filters are these,
Lumiquest Soft Screen Diffuser for Camera with Pop-Up Flash, 11.95 from B&H or
Gary Fong Puffer Pop-Up Flash Diffuser, 19.95 from B&H Photo.
Here is a link to the page showing these and other modifiers for your pop-up flash,
Light Modifiers| B&H Photo Video.
If the pop-up flash is not strong enough you may have to use an external flash or 'speedlight'.
On Camera Speedlight Modifiers:
Redirecting the flash off the ceiling or walls is usually easily accomplished with an speedlight by rotating the head upward or, in the case of better flashes, swiveling the head left or right.
Diffusing the light can be accomplished by many devices. Examples of simple and effective diffusers that I have used is the are the Sto-fen Omni-Bounce and Vello Bounce Dome, esentially plastic domes that fit over the flash. They are available to fit almost every speedlight and are in the ten dollar range at B&H. Start on this page,
Light Modifiers| B&H Photo Video and narrow the search for your brand of external flash.
Enlarging the speedlight light source even further can be accomplished by mini soft-boxes, one of which is the
Vello Universal Softbox with Colored Gels Kit for Portable Flash (Small), which has the advantage of being packaged with color gels, 20.95 from B&H Photo. There are numerous others. I personally own mini soft-boxes from l
Lumiquest and they are quite reasonable.
About Color Correction:
The color gels packaged with the mini soft-box above are for modifying the color of the flash to match that of the existing, or 'ambient', light. This is very important when using flashes that will not overpower the existing light, the most common case when using pop-up flashes or speedlights. Not correcting the flash color, or 'temperature', will lead to a great many off-color problems, especially if the ambient light is sunlight, florescent or very warm incandescent(tungsten). Even pop-up flashes should be matched to the ambient light with gels available on the pages referenced above. Color will probably be important to the dog owners.
A great resource for learning about flashes is the Strobist website. There are a series of easy to follow lighting tutorials beginning here,
Strobist: Lighting 101.
Don't be intimidated by flash, it is really easy to learn to use properly and will greatly enhance your photography. Trial and error,
('chimping' or re-shooting after adjusting your camera), has become much easier in the digital age.
Hope this helps.