Hi, I think that Loki is a great name for a dog as well as reminding me that it's been years since I saw Dogma
However, I do think that it might be a little similar to your daughters name. This is nothing to do with what others might think, but purely practical. Both are two syllables and other than the hard k, could sound similar, especially if called out and emphasis placed on the end 'iiiiiiii'. I suppose I'm thinking that, if you're out somewhere like the park and want to call one of them, it might be confusing for the other. Alternatively, if they both come running, this may actually be an advantage!!!
P.S. We've gone for 'Otto' for our new pup, he's a Dachshund so we thought something Bavarian was appropriate. Husband is a history teacher so we've ended up with, courtesy of a class of 14 year old boys, Otto von Bisbark...!