Nope, if you follow some Khajiit creation theories they were originally bosmer before changing into Khajiit by Azura.
This is accentuated by the fact that if Khajiit are born under a certain moon, they appear as their old bosmer selves. You can even be one in the first ES.
As for a dog-man. It's very possible. All it takes is a grumpy daedra and some hapless mortals.
