So I was just going through the character creation on D&D beyond and realized that there is not one but two Cat type species. Where is the love for Dogs? Has anyone ever done a home brew for a half man half dog or “Mog”? We’ve had a great example of one since the release of “Spaceballs” to use as a template for some time now. Any thoughts on what that race would be like? 

I have a similar one (except it is Viking inspired wolf people), and have found a good deal of dog-person brews you can use. If you would like, I can share those with you (later, since I'm on mobile rn). If you want to make one, you can use the Detect Balance chart as a good starting place.

Some traits I would recommend- 

Keen senses- either prof in perception or advantage on perception checks relying on smell/hearing (take your pick, or both)

possibly pack tactics

maybe advantage on saves against the frightened condition

Animal friendship at will with canines

can talk to canines and understand them

In 2e, in the Mystara campaign setting, on the Savage Coast there were a race of dog-people called Lupins that were a playable race. You might be able to find stuff online to remake them as 5e homebrew.

Here was their MM entry if that helps:

http://www.mojobob.com/roleplay/monstrousmanual/l/lupin.html

Here is info for their PC Race that someone adapted to 3.5e that might also help:

http://www.pandius.com/lupnbred.html

There were different “breeds” (subraces) of lupins, some were Small creatures like Gnomes/Goblins, and others were Large, for 5e that would be Goliath sized so would have Powerful Build. I agree with Avian_Olivine about Keen Senses & Pack Tactics as well.

I forgot that they should also pro’ly have Darkvision, Proficiency in Survival, and an Artisan’s Tool Proficiency of their choice. Maybe give the Small subrace Proficiency in acrobatics to balance the powerful build that a Medium Subrace would get.

I updated my first post.

How about something like this?

Lupin