Maddie, I think the law is 14 years of age to actually start a legal job. That's what it is in NSW anyways, and I've had a job since I was 14. Before I was 14, I did just about anything to earn money. Pet-sitting, dog walking, baby-sitting, making head bands and other crafty items and selling them on Ebay. I really recommend selling stuff on there or etsy as you can make quite a bit if you're creative and selling to the right market. http://psimadethis.com/page/6
That's a good site to get some inspiration.
As far as getting a job in the horse industry, be aware! Some people aren't always as they seem and can be......... I'm not saying all are, in fact very few are, but at your age just be careful. Some will take advantage of your age and sometimes forget to pay you because you're so young they think you won't speak up. They might offer free lessons, experience etc, but if you want to be paid, you need to say that straight up.
When do you turn 14? Your best bet would be to apply for fast food places and retail outlets as soon as you turn 14. Fast food and retail give you customer experience and O H & S rules etc. Sometimes the work can be monotonous, but it all about just working and earning money. YOU WON'T BE GETTING PAID MUCH. When I was 14 I was only getting roughly $7.10 an hour. So for an 8 hour shift I was getting $56.80. That's not much, but if you put it in a savings account and don't touch it, it will grow. Make sure you're ready for a job too. If you're not comfortable about being bossed around, working hard, taking criticism, abuse, random chitter chatter from customers, doing the low jobs (ie changing bins at food food places), then don't apply.