I'm a dog walker and I considered doing this. In the end, I decided not to, largely because... well... :D
When you work as a dog trainer, you're basically working with people more than you are working with dogs.
Unless you become a trainer for a rescue centre or similar, where your job really is to work with dogs one-to-one. That's something I'd personally love to do.
The other thing to consider is your likely working pattern. Evenings and weekends would probably be common, as clients who can afford dog trainers tend to work full time, thus would be more likely to want sessions outside of standard working hours.
Another thing to consider is your confidence with aggressive or reactive dogs.
When I was looking into it, it seemed like the best way into it would be to do a combination of study (take a course, etc) plus mentorship from an established dog trainer. It could be worth reaching out to trainers in your area for a conversation, to get advice, or see if they offer mentorships. :)