First off, let me thank you all for your very helpful and well thought out responses. This has aided me immensely.
As far as whether or not I priced the dogs correctly or chose the right dog as a base, I think I did fine. I used the MM "
Riding Dog " (or "Dog, Riding" technically) which is a medium creature. This seems to match up with the "
Dog, Riding " from the "Mounts & Related Gear" list in the PHB.
So I think the "Fighting Dog" (75gp) and "Hunting Dog" (150gp) when compared to the PHB "Riding Dog" (150gp) is fine. Mainly because I think the "Dog, Riding" in the PHB & MM are the same creature. I'm just changing its skill set. Although comments to the contrary made me go back and check my math, which is always a good thing. Thanks.
As for allowing it as a familiar, I think I will have to say "No" to my player. Not because of stats, because as several of you pointed out, they become a lot less dangerous (other than damage) when they become a familiar. But Thurbane (thanks also for the Special Ability recommendation) and Infiniti2000's comments especially reminded me of size and CR value. Every other familiar is either Tiny or Diminutive and at most 1/3CR. It seems unbalanced to throw a Medium CR 1 creature into the mix; even if it's new stats might knock its CR value down a notch.
As for Improved Familiar as an option, that seems overkill. The dogs all blow compared to what's on the Improved Familiar feat list. I guess I would allow it, I just wouldn't recommend it.
Awesome comments all. Thank you so much for helping me out.