Yup! Now that you've upgraded your front sprocket to a smaller size, you now need to get a smaller back driver to accommodate that change. The mechanical details are a little hard to explain, but just know that that smaller your front sprocket is, the smaller your rear cog/driver needs to be, otherwise you'll be pedaling hard and going nowhere, looking like a hamster in a wheel-cage.
The benefits of a smaller sprocket include a little weight loss, as well as more clearance when doing various grinds or lip tricks (so your sprocket doesn't hit the coping, ledge or rail).
To my knowledge, if you don't already have a cassette, then you're going to have to buy an entire new rear hub (cassette) in order to have the 9-tooth driver. I believe the smallest cog you can get for a non-cassette hub would be about a 12 or 13 tooth, allowing you to run a 33 or 36 tooth sprocket up front.
Check out our product guide where you can find info like this on all bike parts!!!
Just click where it says "How To Choose a BMX Sprocket" to get more detailed answers to your questions.