Don't get a straight out "road bike" if cost is prohibitive. Get her some narrow slicks on that MTB or look at a hybrid with same. At this level it's just to see if she's interested in riding on pavement at faster speeds, over longer distances. Trek even has some adjustable bikes for kids/teens. Or go used. Small road bikes are seen all the time on Ebay. Few people bid on them, so they can be had at a reasonable cost.
Funny how times change-when I was a kid, we were all riding. Our parents wouldn't be caught dead on any kind of a bike. No one had to get us interested-we rode all day long when we could and rode all over town. We didn't have to have "special gear" or be "fit to a bike". It was a bike with 26" wheels and we just rode it.
Maybe take her along and let her pick out what kind of bike she wants to ride.