I think they would both be correct, but different meanings, as with the dog example:
"E giusta la mia risposta?" would mean, "Is it correct, my answer?" -- "Is the answer I gave you the correct answer? Is it correct?"
"E la mia risposta giusta?" I think would mean, "Is it my correct answer? -- "The answer you wrote on the board, is that MY correct answer, or someone elses?"
The two parts (the answer, and the quality of being correct) makes it difficult to notice the slight differences from the placement. So if we remove the second part of each sentence, I think it becomes easier to find the meaning:
"E giusta?" = "Is it correct?"
"E la mia risposta?" = "Is it my answer?