Hi Emma - the moderate resorts don't have balconies. You step out from your room onto a shared balcony, so long as you're not on bottom floor, but you can't sit there, it's just a walk way outside your door.
Did you check rates for Wilderness Lodge or Animal Kingdom Lodge? They have balconies but they're less expensive than the other deluxe resorts. Did you check out the Disney offers - for the US, you can get 7 nights for the price of four, or for the UK you can get fourteen nights for the price of ten.
If you're from the UK, the discounts and park tickets work out better using the uk site.
I haven't stayed at Animal Kingdom Lodge, but at Wilderness Lodge, I've always booked the standard rooms and got upgraded without asking. I highly recommend the extra the WL costs, compared to the moderate resorts - especially if you just need one room.