You'll have to be careful not to spend the outputs that are used in the LockTime transaction, otherwise that transaction will be invalid when your niece goes to claim it.

She will have to store the transaction somewhere that she can find it when the correct block comes along. If she can't find the transaction, she won't be able to broadcast it.

You'll also both want to keep up with any news about bitcoin in the meantime, since (depending on how long a time period you're talking about) there could theoretically be significant changes to the protocol that render the transaction invalid (in which case you'd need to issue a new transaction).