I have a Benjamin Break barrel spring rifle and I will say, I would be leery shooting at anything larger than a raccoon with it... Mine is pretty nice, Shoots "950" FPS in .22 and I shoot the Premiers out of it. I watched a crow take off after I hit it with a pretty well placed shot at the base of it's neck @ 46 yards. I watched the bird fall off my roof, flip around a bit AND THEN IT GOT UP AND POORLY FLEW AWAY. I know this bird died, but I don't know where or when. I was floored. I've thought about this shot for the last 3 weeks pretty constant since it's happened. Not because I am filled with remorse, but because I missed an incredible learning opportunity by not hitting "record". A million and one things could have happened here, but I know I saw that pellet travel and make pretty solid contact.
I will tell you, that your rifle is not going to maintain the ballistic coefficient needed past 30-40 yards to barely take down a raccoon let alone a "small deer". I would recommend downloading an app called Chairgun Pro and look at what all it has to offer. I am not quite sure how to use it yet 100%, but if I am doing it correctly your rifle IF SHOOTING AT 830FPS with 14.3 grain Premiers will have around 11fpe with a velocity of 570ish at 30 yards. This is a very different scenario, but my rifle won't penetrate (barely leave a mark) on a 20oz soda bottle at 100yds that is full and has never been opened (full of carbonation) which you would think would pop it like a balloon.
I would highly recommend you NOT try and shoot anything above the size of a raccoon with that rifle and even that is pushing it for a quick effective kill past 30yds.
I am sure others will come in with more accurate info, but after hanging out here for a short while I've learned A LOT and have just recently purchased a new bullpup PCP that can produce 50FPE at the muzzle which will be MUCH MORE EFFECTIVE at dispatching small to medium game than my Springer that would more than likely just maim anything bigger than a bird at yardage.
I know sometimes you can't control how a shot ends up, but if you are wounding more than killing, that is NO GOOD. Do some more homework and really do the math on what you want to achieve. Obviously a lot of this came from trial and error as we didn't always have all these gadgets to tell us what the outcome will be before we pull the trigger, but wanting to be a better shooter involves more than just sighting your rifle and shooting paper.
This is no way me "scolding" you or trying to be negative towards what you want to do. I just want to make sure you have a realistic idea of what your gun can and CAN'T do.