Hi Luke-
Welcome to Drummerworld, and don't let anything stop you from following your aspirations.
In short, having less functional limbs (or even missing limbs completely as in Rick Allen's case) will give you some disadvantages when playing drums. But it can also create a world of advantages and can allow you to focus on two of the most important aspects of drumming: keeping good time and creating a good feel.
A few years ago I had most of my right hand severed off by heavy machinery. Thanks to an amazing doctor who re-attached it and years of rehab I still have my right hand and it has pretty functional use, though it has left me permanently disabled. Since drumming had been my biggest passion since I was 4 years old, I used drumming as motivation to do all the physical therapy and rehab necessary to get my hand working again.
While recovering I spent 11 months practicing with one hand and two legs and it allowed me to change my focus and approach to drums. Now since you are new to drums, it may take some time to grasp the importance of some of the following concepts, but more than anything I want to encourage you to pursue drumming despite disabilities because: A) Drumming is great therapy for anyone, and B) As you well know, we learn to adapt to our situations and often these adaptations open wonderful, new creative doors.
The main thing that a drummer can focus on - even a drummer who only has a left foot and no other limbs - is keeping good time. Yes, with one arm less-functional than the other it will be harder to play complex beats and mind blowing fills. But you can still develop a rock solid sense of time, and that is what will make people want to play with you more than anything. Instead of spending time practicing complicated chops, spend your time practicing playing to a metronome - even if it is with just one limb - and really listening and internalizing the flow of time. Yes, you can play beats with just one hand. And you can also make a room full of people dance by just playing one simple note on the snare drum (the "backbeat") at the perfect time just two times per measure.
Another thing I have done is developed my well-functioning limbs to compensate for my poorly functioning right hand. Most drummers have a right hand that can play faster and more complex patterns than their other limbs. I made it my goal to try to get my left hand and two legs to play the speeds and patterns that my right hand once played. It has opened many new doors.
I embraced the "less is more approach" and found that playing less notes at the perfect time, and therefore allowing more space for the other instruments to play, was a simple and easy way to make the song as a whole sound as good as it can be. My disability has also opened up the world of linear drumming (a concept that you may not know as a beginner), and this approach to drumming has helped me create a style that is more personal than any style I had in the decades before I was injured.
A member of this forum also has a great website: handidrummed.com
I don't know if it would benefit you, but the only reason I'm able to play with two drumsticks/two hands is because of a drumming glove I found on the internet: drumglovemusic.com
Luke, please send me a Private Message with any other questions you may have, and if you send me your email I will send you an partial article I have written on drumming with 3 limbs or less.
I have more I could share but that's too much 6-fingered typing for me right now
-Alex