oh sorry..ok i meant reflecting the flash off a surface so that the lighting from the flash will not be a direct harsh one, and will be spread more evenly on the subject. But it is not achievable with the camera's internal flash cos the direction of it is fixed, and usually it isn't powerful enough.
If you camera supports external flash, and if you do get one in the future, trying bouncing the light off a bounce card, and I think the red-eye problem will be reduced or resolved. I've tried it for my dog and it worked very well.
Or one other thing you can try is to take your dogs from the side, so that their eyes are not directly exposed to the flash. But that will severely limit the kind of shot you can get, so not very flexible.
I have a PS NoRedEye Action. I can email to you if you want. However, this works quite well with human eyes only. Tried to do it with your pics, turned out even worse than your later pic.
Another way, though tedious, but definitely will work is to have a pixel by pixel correction. Use PS6 to manually overwrite the unwanted portion with the colour that you want. You can select the surrounding pixel that do not have any red eye effect and get that colour to go over the affected ones.
This is time consuming, but with practice should be able to do it within 15 minutes per picture.
Red eye in humans is caused by light reflecting off the tapetum lucidium, a layer just below the retina that is filled with blood vessles. When an intense light such as a camera flash firing occurs the eyes pupil contracts but too slowly to stop the reflection of the redness of the tapetum.
Red eye is guaranteed to occur with the human eye if the flash is located less than about 2.5 degrees off axis to the eye.
Animals such as cats and dogs have eyes designed to see far better at night than us poor humans, so they have a different physiology of the eye. The 'red eye' and silver 'eye' are actually caused because they have a far more reflective tapetum lucidium than humans have. The tapetum lucidium in most animals that are nocturnal or have evolved from notcurnal animals reflects light back on to the retina and it's rods and cones thus increasing their night vision sensitivity.
The angle for red eye in animals varies greatly depending on the animal species, the size of the eye and how dilated the pupil is. As a general rule where possible use bounce flash off the ceiling or flash located a foot or more to the side or above the camera to eliminate red eye and silver eye from animal photos