Hiya! I adopted my dog, Gruedle, a couple of years ago from the local animal shelter. She was severely abused by someone, but is well loved now. She only weighs 9 ponds, but has the strongest prey drive. She also is very speedy and highly intelligent. Could she be a lurcher?
She is very small for a lurcher, but also very cute! With a strong prey drive I would think there is terrier of some kind in her background but I really have no idea. Which part of the world did you adopt her from? Hopefully someone far more knowledgeable than I will be around shortly and can help you more than I can. Oh, and welcome to Breedia from Tikki Tikva and me!
Impossible to say, but there could be something like small Whippet or Italian Greyhound x Yorkshire Terrier in there, so I guess that might make her a Toy Lurcher, - if there is such a thing. She is a lovely little dog though - I bet she can gallop!