Please don't buy a bar that stands up by itself. If your daughter is doing any kind of big skills then she will need a bar which ties down with anchors like the ones at gym.
My cousin is 4 and she has a bar that was bought off a gymnastics website as a gymnastics bar. These bars are only good for little kids who can just swing on them, and maybe a few small casts. If they are put up high enough for any actual skills, they just wobble. If you do a bigger swing, back hip circle, etc, the whole thing moves or even falls over. The only way it works is if you have 4 people standing on each end of the base. Or you could use some really, REALLY heavy weights instead maybe?
To have a bar at home, it would need to be tied in by anchors like what you have at your gym. It would probably need to be in a permanent position. The best option for outdoors would be a metal bar, in this case you would want it to be tall enough for giants.
Alternatively, like
@Dahlialover said, a playground bar could be an option. I have one attached to some monkey bars at home, and I used to use it when my routine was just swings, pullover, back hip circle, etc. Now days it really hurts to do a big cast or come back to the bar hard because there is no bounce, it is stuck in place, and also it is too low for me as I have grown. This could be an option to just have some sort of safe, solid bar.
At my old school there was a metal playground bar which was between two pieces of play equipment. It would've been definitely high enough for giants and castaways, don't worry, I didn't bring loops to school to try it, but speaking
A wall bar is a great option for chinups or leglifts. Don't put then down a hallway for example, they are not designed to be swung on and WILL fall off the wall, you WILL get badly bruised or much worse!
So those are your options. A bar at home is a difficult one. It really depends what level of gymnastics she is up to, what she wants the bar for, etc.
Do you have a beam? Beams are great for at home use. You can get a little half height one, they are good quality and can be kept indoor or outdoor (with a risk of touching the roof indoors of course). You could offer her that instead maybe? AirTrack's are also great for at home, and really good for waterslides when they are wet as well (does anyone else use their airtrack as a waterslide or just me?!
Here are some photos. L-R: First photo is a big no for any kind of bigger skills. Second one has a longer base, I haven't tried but it could be more sturdy, but check the base and height most importantly. If you do choose one like this, you MUST have a huge, long base or it WILL fall! This is the same in image 3, it looks to be working ok for the girl because this bar has a huge, heavy base.
Alternatively there is of course a metal bar. I think this is exactly the same monkey bars that I have with a bar on the side. It is a little short but a taller one would be ok. Possibly bars like the one in the 5th image could work ok too, you could get them put in at a higher height maybe?
Then the last image is of a wall bar. You can get ones like this that attach into your doorframe, don't leave a mark, and are easy to move around. No screws are required! Just PLEASE DO NOT open the door and swing on them, they WILL fall off! I find they are also good for leg lifts as you can close the door to have a wall behind you. Unless you are really tall you can just walk under the door underneath them.
Good luck!
