I've been a handler for seven years and have worked in LE for almost 20 years. My advice is to focus 100% on being the best cop you can be first and foremost.
Per policy at most respectable agencies, you probably won't even be eligible to apply for a position as a K9 handler until you've put in 3-5 solid years of patrol work and you've proven yourself as a good decision maker, dependable, and, frankly, an above average performer. Focus on being not just a cop, but a great cop, first.
You've got to stay in shape. No need to elaborate here. I hope.
Believe it or not, the fact you've got other dogs could potentially be a detriment. That will depend on you, your agency, head trainer, policies, individual dogs involved, and a host of other variables, but don't expect to get any sort of preference because you've got dogs at home.
Don't assume or take for granted that you'll EVER be assigned to a K9 team or unit. Hopefully you understand that and you're starting a career in LE for other deeper reasons. If K9 is a career goal than great, just don't let it be your driving motivation for pinning on a badge or you will be met with a massive disappointment.
Finally, if you have solid reasons for joining LE, you are committed to maintaining physical fitness standards, and you get out there and establish a good reputation on your department, establish relationships with the guys on the department's K9 unit. Ask to attend training days (voluntarily - on your time). Watch, listen, learn. Ask to attend a decoy school. Lay tracks. Prove that you are committed and that you will put in the work to get a dog. Study K9 case law. Know your department's policies and paperwork related to dog work. There is a lot to it, but like anything else in life and career, you'll get out what you put in.
Living with these dogs at home can sometimes be like having a pet, but understand they are NOT pets. They are arguably one of your department's biggest liabilities and they are serious, expensive, working dogs that generally are trained as a force response option.
If you want a big cuddle buddy, being the dumb half of a K9 team isn't where to look. My current dog gets along with the other dogs, cats, and livestock/farm animals on my place just fine, but he's never permitted to be anywhere other than his kennel if I'm not around. He doesn't wander around my house, sleep in my bed or the couch, or eat anything besides what I give him. Different dogs, policies, laws and circumstances will dictate.
Good luck, hope that helps and I hope I didn't discourage you. There is a lot to it. A lot. It took me a long time to get a dog, but I wanted it bad and even left a plain clothes detective role when a vacancy popped up at my department. I haven't regretted it.
I used to say that being a handler was the most gratifying and fulfilling thing I had done in my career, but now that I'm assisting with firearms and training at my PD, I'd say it's a tie. Ymmv. Again, good luck.