Black Mouth Cur!
They almost do it all, although, I did have an Australian Blue Heeler, I found in the deep woods in sub-zero weather and this girl could hunt squirrel.

A lot of squirrel dogs will just run to a tree, the rat climbed in and just sit under the same tree.
Not Holly! She would back up, circle it until she could get a visual on the rat and let me know she saw it with a low bark.

With her circling the tree, the squirrel would try to avoid her completely, and go to the other side, unaware I was waiting to lower the boom.

When I found her in the woods, she lived on a diet of acorns. She had a way of cracking the nuts with her teeth, then using her paw to get to the fruit. Not only that, she would run up dead trees or any tree low to the ground after the squirrel.

For some reason, she had a dislike for squirrels! I can't tell you how many squirrels she would bring back to me, dead, where she ran them down and break their back.

I miss the 'ol girl, even to this day!