Good suggestions have been posted but I still wanted to throw in another, or two.
While many have had a good experience in year round swimming, I believe it depends on the program SHE will be using. As a mother, kids race director and strength & conditioning specilist, it is my opinion that year round swimming programs tend to burn kids out and some may contribute to overuse injuries. Make sure you pay attention to how much they are swimming (distance and days in a week). Year round usually means they cannot participate in any other sport which is something I would never recommend to a child at any age. However, swimming is very important to a triathlete and one discipline that scouts will look at when choosing triathletes for a youth development program. See if you can find a program that offers something in between your current once a week swim to maybe 3 swims a week, but give her a break now and then.
Running up to her race distance, or a bit over, 3 times a week is fine. Same with cycling. If she wants to get faster then make sure you ride with her, rather than run, so she can achieve faster speeds.
She still believes training is fun, which is good. It shoud stay that way. If she does not want to do it you can give her a gentle reminder of her goals, but I would never push her. Also, the recommendations to be in team sports is very important. One thing I tend to remind parents is how much we played when we were kids. We were constantly moving maybe 5 hours a day! The key word is PLAY.
My kids (9&11) are triathletes but are not competitive. They are mainly into team sports such as football, baseball (boy) and baseball (turning into softball this season to play with the girls), gymnastics and volleyball (girl). However, we usually get in a run and ride 1-2 times per week and swim on a summer team. They ride where I run and I let them go ahead of me (I can see them the whole time since it’s on a trail) for sprints and meet me back so their ride is faster with more distance than my run. Their runs are usually intervals of about 100 yds or so (with slow jog or quick walk recovery) since most of their activity is shorter distances, but their total distance is usually a bit more than their race distances.
Also, since kid tri courses vary, I would highly recommend her riding/running the course a couple times before so there are no surprises. I have seen tris in a parking lot with many twists and turns to courses that are hilly. Just like you would be prepared for your race, make sure she is, which in itself will make her a bit more competitive.
Good luck and feel free to email me if you need anything else.