Do you think this is a cairn mix?

[HeidiM]

 

Hi all, I just adopted an 8-week-old puppy from a poodle rescue. The foster mom said she believes it's a "terrier" and poodle mix. The mom & dad were found together and mom was already pregnant. I'm trying to figure out what type of terrier mix my puppy is. I think she's a cairn because she has the wiry hair growing in with the eyebrows and her coloring. She's 4.4 pounds at 9-weeks-old. 

The first two pics are the mom (she's the fuzzy wiry dog in the first pic). Is she a cairn and just really unkept? The next two are my puppy, Daisy. The last one is Daisy's father.

I've adopted and raised several puppies, but I'm not familiar with terrier or poodle breeds. I'd like to figure out what type of terrier she is so I know what to expect and how to train her. If she's strong-willed (I think she is) I'll need to be more proactive about training. Also, she is a digger. I read to give them an area of the yard for digging and teach them to only dig there. Right now she's trying to dig into my sofa!

Thanks for any input!