I haven't used a Target gift card to buy another gift card, but it looks like the PP has the answer for you. If you run into any trouble, use the Target gift cards for the groceries and household supplies that you would normally buy out of your regular budget, then use that money to buy Disney gift cards. Many times when I get a gift card, I take the corresponding amount out of the budget to buy a Disney gift card (especially if I get a Target card, since I buy so many things there anyway, but also if I get a restaurant gift card - I take the amount of the meal out of the budget and buy a Disney card).
If you have a Target credit card, you can get 5% off the Disney gift cards there.