What design does my study have?

Say for example I wanted to do a study comparing cats (the control group) and dogs, measuring the extent to which they exhibit 4 behavioural variables.

My initial graph should display the differences found between the two groups, but then I want to dig further into the results.

In my dog sample, there are two breeds, and I want to compare them with one another, this time excluding the cats.

Does my IV then have four levels? Control, dogs overall, dog breed 1 and dog breed 2?
Does my DV also have four levels - the four behaviours?

I am looking both between and within subjects here, right? So is that a mixed design? Please help! I've consulted my usually trusty textbook but don't know where to go from here...
Which textbook are you using?

Do you intend to compare (e.g.) dog breed 1 to aggregate dogs? OR dog breed 2 to cats?

If not you may just want to consider doing separate studies for the differences in carnivora (cats and dogs) and differences in canidae (dogs 1 and dogs 2).