At eleven months, you should be able to do just about any type of exercise (assuming your bone growth is proceeding at the average pace!). It will be important going forward that you do exercises that will keep your core and back muscles strong and stretched.
I do the usual exercises for core and back that most PTs give to their patients. I also bought a yoga DVD specifically designed for people who have had back surgeries. Many people swear by Pilates but you really need to take a class under the supervision of a certified instructor so you don't end up hurting yourself.
With a lurabar fusion, you generally want to avoid anything that puts the spine in extension (bending backward). Depending on how you swim, this can include some swimming strokes that are done on the stomach.
I had some segment reconstruction in addition to my 3 level fusion and I will always feel I need to be careful in selecting my activities. But I know people who have resumed all their former activities, including mountain clirabing, kayaking, running, etc. I didn't do those things before fusion, so now would NOT be the time to take them up!!
I guess regarding the conflicting advice you've received from PTs, if you've been told you are fused, gingerly try what you want and let this adage guide you: "If it hurts, don't do it."
One more thing -- try to rotate activities so all the various muscles get a work-out over a period of time. Keep your muscles stretched out and make a point of always using good body mechanics and posture.
When people get into trouble after a successful fusion, it is often because they are "good" about keep up their PT activities for awhile, are careful about gaining weight, posture, mechanics, etc. but then, sooner or later, they revert to all the old bad habits -- stop exercising, slump on the couch in front of the TV or video games for hours at a time, use poor posture when sitting in front of the computer, eat too much, and before they know it, the back starts hurting again....Just keep reminding yourself, "once a spiney, always a spiney." There are things you need to do to keep your back strong and healthy.
Good luck. Hope you find some activities you enjoy doing and find the time to do them!