There are lockers available in the Magic Kingdom under the train station. There is not an area to change, you would have to do that in a bathroom. The lockers are not so large that you would be able to hang up long clothing, though. You only pay for the locker once, so you could carefully put your nice clothes in the locker in the morning, then enjoy the park for a while, and then change into your nice clothes and relock the locker, then use it again when you return.
It could be a long, hot day in the park, so maybe you would want to go early and stash some casual clothes in a locker, then hop back to AKL to shower and change, then go to V&A, then back to MK and retrieve the casual clothes. Plus, it is always nice to have a short break from the parks. Get a drink at the bar in AKL, I think it's called Victoria Falls Lounge? We loved it on our honeymoon.... they were heavy handed with the liquor, so much so that my DH needed more Coke in his Jack & Coke!! A first and only!!