As Jeanne says, you need 3-5" extra on all four sides. The reason the longarmer needs the extra is to allow pinning to the roller canvases top and bottom. On the sides the extra is needed to allow for clamping the sides to hold the quilt taut(but not too taut). I have quilted even if the sides of the backing are exactly the same measure as the top but it can be tricky as you have to sew very carefully around the clamps.
So, it sounds like your 9" top and side(giving you 4.5" each on four sides) will work fine.
By-the-way, if you are ever short of fabric on an edge you can add a strip of scrap fabric that can be removed later. With this method you do need an inch of backing fabric to add the scrap strip to so you would not affect the top(otherwise you'd have to trim some of the top). I usually have enough extra beyond the top that I can just cut off the excess but sometimes I've so little extra backing beyond the top I had to remove the stitches of the scrap strip to release it. When I sew the scrape on I use a large stitch which will be easier to remove later. I don't like to do it this way but it has worked for me a few times and allows you to use the backing and not have to get another.