It seems to me you're going down the right road as far as your D's musical interests.
As far as the recording issue, it's really not as super expensive as you think. Are you going to record her with a full band or will this just be a solo recording? Of course if you have a band you have to pay the musicians. That's something to factor in. And for shopping to publishers it's not really necissary to have a full band arrangement. If you're looking at giving stuff to publishers then realize that for the most part publishers will be looking to place the songs with other singers. So, really all they need is the basic form of the song with a piano/vocal or guitar/vocal recording.
Of course a full band recording sounds cooler and more "official". However, at her age, and with her work ethic..her best stuff is probably yet to come. So if you pop for a full band recording she may find that next year her writing has improved and then she'll want to record again.
Also, if you get serious about shopping her around make sure she can handle rejection and take it for what it is. That's not to say there's anything wrong with her but in this business once you commit yourself to trying to achieve higher levels of success, you'll hear no many times before you hear yes. It happens to everyone. Even the Beatles were turned down by label after label before somebody finally gave them a chance. So hopefully she realizes that and can handle it well. The music stuff is great but when you get the business side involved with it, things can get ugly.
Anyways, take it slow with her now. She's only 12 and her stuff will only get better. Keep her going and let her record, and take her as far as she's willing to go now, and as far as you're willing to let her go. But much like saving marriages...you've gotta be patient with these things.
A dream it's true
But I'd see it through
If I could be
Wasting my time with you
-Band:Phish Song:Waste