I've fed both of mine almost exclusively off of one breast in the earlier days and then entirely from one as they got older (my leftie too). DD1 fed till just after 3 and I'm 12months in with DD2 (6months of that was tandem feeding too), neither have ever had any formula, bottle or supplementation so it is definitely possible. Breasts work on supply and demand so if the baby is demanding more from one breast it will make more to keep up.

The only real annoyance for me has been my breasts are completely different sizes which makes bra selection difficult but no problems actually feeding at all.