It is true that it is absolutely essential a child have opportunities to hear and use the language for it to be retained - however, many of the answers here seem to focus solely on the development of fluency in a foreign language as the only worthwhile outcome of such an exercise! I really have TWO responses for you.
Using Langugae Programs With Kids and In particular, Rosetta Stone
I am not familiar with a children's Rosetta Stone program but if they have one, I've only ever heard quality comments about their products and would assume these would apply. If you are speaking about already owning the adult program and using that with your child, you may find it irrelevant and dry for your child (although he or she will still learn from it and from watching you use it - even if the lessons are more about learning how to learn than the language itself).
Adult language programs usually begin with travel lingo - how to make hotel reservations and find your way around the city and the like for obvious reasons. This vocabulary simply isn't relevant for the young who would rather know how to ask for a crayon and a cup of milk to go with those cookies. I would personally stick to a program for kids (OR go through the whole program yourself - while your child watches and listens in on occasion and then use what you've learned with your child and in conjunction with Children's books in the language)
We have used the BBC's Muzzy program. Very happily, we live an area where there are a lot of Spanish speakers and though he is not fluent, my husband had Spanish in school and watched the Spanish videos with her. This way, they can use Spanish together. She can do well enough to help her dance teacher translate when necessary. I have not used German in over 15 years, but spoke it as a child. About three months ago, she and I started German with Muzzy together. Now that she is six, the written language computer games have been essential in order to keep her challenged. She also hears Berlitz lessons (that I'm using for myself for review, but she hears me doing and practicing with the disks often).
As for the amount of time, "The Bilingual Edge" says that for a child to become fluent in a second language, language exposure must amount to about 80% of their time when learning a language outside of an environment where they are exposed to it with media, street signs and other speakers around them. If you learn it together, you are not immediately aiming for fluency, but you may want to know that figure so that you can do some extra work to create the richest language environment possible. For example, I have children's books in German left over from when I was a child she now has access to and we have set up a system like what we used to call "pen pals" but it is "Skype pals" with a little German girl we will start regular language dates with in another month or so. The little German girl is learning English so they will take turns alternating the languages used.
The Value in Working Toward Language Aquisition Even When Done Without Native Speakers and in the Home
The opportunity mentioned above with the little German Girl came up because we started German and the opportunity fell in our lap when the mom was doing some graduate studies in the states where we were and found out I had once spoken German fluently - for a child that is (although I'm pretty rusty). Since I provide child-care services in the summers, I was the right candidate to care for her child. Now they are back in Germany, but we have a resource (and friendship) that may not have been available to us had we not already begun our language adventure.
I had similar experience when I began learning American Sign Language. All of a sudden, my brother in law started dating a translated, a new teacher at the school turned up that was deaf (but read lips and had a cochlear implant), AND our new librarian turned out to be deaf. You never know what might happen when you open that door.
My goal with my own little girl is not necessarily fluency, but functionality and at least a laying of the "groundwork". She can eventually choose a language she would like to be fluent in and learn it in whatever way we need to make that happen. Exchange program, Peace Corps, whatever. Whatever language she chooses in the end, because she will have a background in how to learn another language and how different languages have different grammatical structure, idioms etc. It will be easier for her to learn her second language of choice than if it was her first exposure to foreign languages.
To sum it all up - why not give it a shot and see what happens. Even if your child walks away not having retained more than hello, goodbye and thank you, it is not a waste of time to have taken the time and taken advantage of the opportunity to learn some other - unrelated lessons along the way.
Link to Book: The Bilingual Edge