A person regardless of age can own real property (including a 1 year old). That is universal in all states. And that is actually something that happens fairly often when both parents die at the same time. Of course, a guardian or trustee is usually appointed in that situation who will hold the property for the child until the child reaches majority.
If you wanted you could transfer your ownership to your kids by deed. You could actually do it without a closing but I assure you don't want to do that. The deed transfers ownership. The closing achieves making a public record of that deed in the recorders office and getting title insurance that protects against any challenges to the ownership. Absent that public record, creditors and others can continue to rely on the existing public record (the transfer to you) and record liens on that property if for some reason you are unable to pay debts. And those liens will have priority over that unrecorded deed.
You can transfer by will. Or you can set up a trust to receive the property upon death and then held for the benefit of the children. Or you could set up a trust now, transfer title to the trustee (often a bank) and leaving you and your children as beneficiaries with provisions that they become the sole beneficiaries upon your death.
In other words there are a lot of ways to go about transfering ownership, but...
1. It really requires you to get counsel first. Try to do things yourself and much can go wrong. For example, the tax implications of the transfer have to be considered-- possible gift tax implications and also states may have transfer taxes on any real property that you may be required to pay.
2. You can't really do it if there is an outstanding mortgage on the property--the lending company will not accept a transfer absent pay off of the loan.
2. Transfering ownership has little to do with whether a person can make reservations. Your sales rep was wrong technically when he said a minor could not be on a deed. At the time of initial sale by Disney that might be true simply because Disney requires the buyers to be 18 or older and it will transfer ownership by deed only to the buyers. But you can transfer by subsequent deed.
3. You can designate on Disney's records anyone as the person who will have the power to make reservations even if the person does not own the property; however, that person must be at least 18. In other words you don't need to transfer ownership if that is what you want to accomplish and in fact simply transfering ownership does not accomplish a change in the designation--Disney has to be informed to make a change on its records. In other words, what your sales rep was actually trying to tell you is that the person has to be 18 to make reservations. P