Hi Winger,
If you do a little more research into ACL reconstruction you'll be able to make a more informed decision about whether you continue conservatively or with surgery. Reconstruction is generally recommended for younger active people, but older people tend not to have the surgery.
Reconstruction surgery would usually recommend no impact exercises until about 6 months post-op although some surgeons' protocols start about 4months. You shouldn't really be starting to play rugby again until 9-12 months after your surgery depending on your recovery and rehab, when your knee is very strong and the new ACL ligament has healed into place and strengthened (there is a period of time when the ACL is newly implanted that it's strong but your muscles are weak, then as your muscles get stronger the ligament actually needs to degrade and rebuild in it's "new home" - this is the point when most people who re-rupture the ligament do it because their muscles feel good but the integrity of the ligament is at it's poorest - this is about 3-4 months post op). then after about 6 months you can start gentle light jogging and straight line work. about 9 months is starting to do sport specific drills and higher level stuff before return to sport. Average person will take 12 months to maximum strength and recovery, elite athlete, about 7 -9 months depending on how long between injury and surgery, type of graft, pre-op strength, and type of sport etc.
If you choose to NOT have the surgery you do run the risk of further joint damage because your knee doesn't have the usual ligamentous supports without an ACL and there will be much more unusual movement at the joint. Plus you're not going to be as stable with quick maneouvres and turning. Your physio should be able to explain this more. Your current exercises need to be strengthening your quads, hamstrings, glut (medius especially) and working on your balance.

At the age of 19, I'd probably recommend take the season off, do the surgery and the rehab really properly, and then get back to rugby in a year - by no means should your playing career be over just yet but be patient if you want your knee in top shape for the long haul. I can't stress enough that it's so important to see your physio for a proper assessment and advice.. if you don't trust your physio at the moment, find one you do trust!!!