Get a chalk board or one of those dry erase boards where you can write on and wipe off (Even if your DD can't read this will help YOU
).
Write the verse or phrase of the verse on the board. Over mealtimes or other times (does DD help you in the kitchen?) when you are together. You read the verse together, with you pointing to each word as you go at least some of the time.
After you have done this a few times, erase a word (an easy one like the or and or something easy to remember). Then repeat the process a few times. Erase another word. Same thing.
This breaks down memorization into a slow process where you only have to remember one NEW thing at a time.
This is how we did it in Sunday school when I was a kid.
and yes, for Mat 7:7 you would say, "Mathew seven, seven." To help her understand how the Bible is put together you can also say "The Book of Mathew, chapter seven, verse seven" until she figures out what all those numbers and things mean. (you can show her in your bible how each verse is labeled...I'm assuming even if she can't read yet, she can at least understand the basic principle of how to find verses, and knows numbers etc).
I am a little confused as to why you chose this school for your daughter (one that insists on a Bible translation that you don't understand) instead of other schools. I would think that a Christian school that insists on the KJV has some pretty specific beliefs that a parent would be expected to share, to ensure student success. But that is probably off topic.