i have an all-avoidance team i use sometimes, using spring rabbit
which has identical stats as DMR but lacks the well-known acronym name
i use nordrassil wisp
with it, there is a 357 speed s/s that mine sadly is not, but mine still is faster than the opponent more often than not.
i have experimented with 3rd avoid pets of different types, the obvious idol, also mr bigs and thunder tail flapper, both have blocks that block you too, haven't found an ideal but most important is something to switch if they counter rabbit &/or wisp.
i agree with what was mentioned about direhorn, so many ppl use it and rabbit can't do much against it. my avoid team is something i switch to if i get the same team a couple times in a row and can't beat it with one of my main teams.
best thing about fast rabbit, it is a great counter to val'kir, and to ghostly skull in darkness teams. imo not much of an all-around pet however.