You state, "I should make a almost full recovery over the course of the next 6 months to a year".
Scenario #1: let's say you tore your MCL during your sports day. You have surgery, and the doc expects you to make a full recovery. After a year's time, you have no limitations whatsoever, and continue your military career without any further symptoms of any kind. You even go back to playing all the sports you previously did, including being a butterfly-style goalie for your unit's hockey team.
Is there a permanent impairment or disability resulting from the service-related injury? No.
If you make a full recovery from the injury to your leg, from which you have no further limitations or pain or symptoms, the chances of receiving a favourable decision on your claim application are not good.
However, Scenario #2. Over the course of a year or two, the ligament doesn't heal or recover post-surgery. You are now hobbling along, you walk with a limp, and continue to have symptoms of pain and such. You can't go back to your previous level of physical fitness without having knee pain.
Based on this loose example, you would now have a permanent impairment of your left knee MCL, which could open the door to disability compensation - if the injury to your leg during a service-related event results in permanent impairment or loss of knee function.
All this to say, sure, submit the paperwork. Make sure it is backed up by a CF 98 and other medical reports, including any surgical, physio, etc. A doctor's opinion would also help in demonstrating a permanent impairment.
BinRat55 and Teager make excellent points, to which I will add: BPT have your claim denied at the first attempt, specially if the doc has it written somewhere in his/her report you are expected to make a full recovery.
The VAC disability benefits program is intended to provide financial support for members who have suffered a service-related injury or illness. The program is centered around an injury resulting in permanent impairment and permanent loss of function, not in something temporary which will heal and go away.
You will need to have a confirmed diagnosis of the injury/illness, as well as confirmation from your medical care provider you are still disabled to some degree as a result of the injury.
P.S. BTW, for VAC disability benefit purposes, there is no "dominant" leg. Dominant hand, yes, and the remainder of the upper limb as in your dominant side, will receive greater compensation than the non-dominant hand/upper limb...but there is no dominant leg for VAC purposes.