I think she will love it. The audience sits very close to the characters on stage which is only a few feet off the ground. There are some interactive elements that fall from above as well. If you don't mind spoiling the fun for yourself, you can see clips on
youtube of the show, as well as any other attraction in the park that might sound interesting for her. As far as outdated, the show hasn't been updated since it started, and they still have the old voice of Barney, but since you have been watching the older episodes, this will be more familiar to her than the new Barney voice anyway.
Barney's Backyard is a nice indoor (air conditioned!) play area with some slides, things to climb on, things to jump on, push etc. You can also meet Barney here right after a show (technically you don't have to go to a show to get in line, just time it right). Special Tip: BJ and Baby Bop do not do pictures after the show like Barney does but they are usually out with Barney in the backyard area or by the fountain/preshow area before the first show when the rope for Kid Zone drops (usually around 11, can be earlier depending on parades/park hours but I think an hour before first show on the schedule for that day would be safe.) Least crowded time to meet the characters (sometimes you might get a lot of 1 on 1 time) compared to waiting in line with everyone else in the theater after a show. There is a Barney store connected to the backyard area as well to pick up some items for her.
As far as other things to do to make the trip worthwhile (besides watching Barney multiple times as most kids in that phase will want to do!)...There is a nice short show in Kidzone area called Star Tunes with several characters (Scooby, Shaggy, Woodpeckers, Curious George, Man with Yellow Hat, I think that's it?) and then you can take pictures with them afterward.
You can also have her meet lots of other characters around the park for pictures if she is not scared of them. Check other posts on this forum for the list. Madagascar Penguins meet near this area as well.
The Kidzone area can be fun for the little ones, Curious George area is a wet play area that is good if it is not too cold. At the back of Curious George (you can make it without getting wet) there is an indoor ball play area. I don't mean a ball pit, but a lot of interactive devices you can place soft balls in that get shot up in the air and do other things too. Fievel's play area has more dry fun, a big playground. They do have a big "water" slide you can ride down with her in an inflatable small boat. (I don't remember really getting wet)
Jimmy Neutron might be fun for her as mentioned above. I did have then 4 and 7 year olds balling their eyes out on that ride though, but they were in non stationary seating. Not sure if it was the movement or the movie that scared them? Maybe see if there is a youtube video as well and decide for yourself.
If you get a 2-park pass, take her to IOA and do the Dr. Seuss area, lots of fun interactive areas to walk through and some slow kid-friendly rides like a carousel. (but check height requirements, some have them) Also a show with Dr. Seuss characters and meet and greet after. IOA also has a playground area themed around Popeye.
Hope that helps!