You've had a stroke of luck here.In my experience, clogged tub drains are simply from hair that is caught in the screen or stopper. 

Pick a strategy that you feel best pushes you towards your goals and get laser focused!

Commit and be laser focused.

I’m currently a hairstylist and as much as I love it I have always had a passion for Real Estate more.My question is, if I am to get my license would there be a way to transition out of hair?

Think of all the coffee shops and hair salons with 2-3 floors with a couple apartments above them... these typically don’t hit Zillow so you’ll need an agent for MLS access and don’t be surprised if 90% of agents don’t know what you’re talking about. 

I charge a $350 non-refundable pet deposit since I feel at the very least I will have extra cleaning such as a professional carpet cleaning to make sure dog/cat hair is completely removed and even a faint smell is gone.

IE dog food, dog hair on the couches, backyard looks like a dog lives there, or anything else such as your hard wood floors are showing damage I would send a 3 day quit letter and start evicting them if they don’t dump the dog.  

That level of work is needed to avoid getting bugs and smells and hairs in the house.Look at the renter and see if you think they will put in the level of work needed to care for that many pets. 

I am curious though if the couple was a dark haired woman with a skirt and a blond-ish man both casually dressed.

I go into her room and she has 2 fans going, an alarm clock, an Iphone charger, all hooked up to the same power strip and (the kicker) her hair dryer.