What design does my study have?

#1
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...
 
#2
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).