Ok my 13 year old is starting to run barrels and she knows how to ride but she isn't confident enough to run like she wants to she wants to go fast and her mother and grandma want to buy her an automatic horse and I think she really needs to learn how to ride and be a cowgirl and that way she will have the confidence to ride any horse that she gets on and not one that will do everything for her but I could be wrong what do yall think ? 

Can I say BOTH

She needs to learn proper horsemanship BUT getting a good seasoned horse is a great confidence booster for a kid. With that being said, I would NOT go out and get her some 1D rocket---get a 3-4D been there done that horse.

There is no such thing as an automatic horse . I recommend an older horse that will go the speed she's comfortable at that she can learn to guide and ride. There are some great teenage horses out there that can do wonders for confidence where a kid can learn and have fun before they step up . 
You need to find a trainer that she can take lessons from on her horse and that can coach her when she competes. 

I agree with everything that Mighty Broke said.

Ok thank you for answering my question . Now this is thing we don't have the money to keep buying her horses she is only getting one horse and I don't want to get her a horse that is getting to be to old that it only has a couple of years left in it so what do you think would be a good age that is still fast enough where she can still learn a lot from the horse and not get discouraged because it's to slow to win ? And thanks for all of the feed back I appreciate it a lot .

Where are you located ?

I would really really recommend finding a reputable person (DO RESEARCH FIRST) to help you in your search. So many in your situation can be taken advantage of. 

With that being said----YOU WILL have to buy more than one horse---FACT. Buy her a nice horse in its early teens---she runs it for a couple years and then you sell it to the next parent for it to teach their child and you buy something a little better and hopefully keep climbing the ladded getting better and better.

As Mighty Broke stated, buy an older one, let her go as far as she can on it and then move on to the next level horse.  Those first horses are a great investment and will always be in demand and you will most likely get your money back when selling.  Don't get stuck in the "one horse" mentality, it won't work that way.  Think of learning to run and ride barrel horses like playing ball.  Start out in T-Ball then little league and so on.

I totally agree with what everyone else has said. I also want to bring up another point on the "only one horse" view point and that is horses get hurt. I am going through that right now as I bought my dream horse, put the time in to slowly get with him, and literally the day I was going to enter him he started showing hind end lameness that we have dealing with for six weeks or so. I have only owned him since July and the sellers were 100% reputable....what I am getting at is to some degree it doesn't matter the age of the horse, one small misstep in a run or playing in the pasture can cause months off or end careers. 

Hands down, 110% this.

Mighty Broke is on a roll with advice.  That being said.. I'm an old lady and my favorite horses to ride / run are double digits in age.  There are plenty of older horses that can clock given the rider has the ability to ride them to that level. 

I like a horse to take care of the rider and step it up when a rider is ready.  Those good horses for the youth to learn on and progress are always in demand when a youngen grows out of it. And that growth is a competition level growth.   

It's always a case by case thing.  You do need someone that is reputable that can help guide the process.  Regardless - you are investing money in a youth to develop.  You are also investing in a horse - that is a perishable item, like eggs.  Regardless of age - something could happen and you are looking for another horse.

it wont make any difference on another horse if the confidence isnt there. if you video her runs and zoom on body/ hand placement she can analyze what she is doing wrong so she can change up to help herself and the horse remember  they are a team. it will also help in spotting where she can speed up more and where to check down. when you can see what is happening vs being told what is happening is a big difference in how you run.