Bedtime!

First time mama here and I have a 2 month old son and I am wondering what time I should be putting him down for the night. Typically it's been late (like after 10) usually close to 11 or 12 and sometimes when he's really difficult 1 or 2 in the morning. 

I am just wondering if I should be trying for a "bedtime" for a baby that young or keep letting him go to bed later. (The selfish part of me wants him to go to bed later because then we all go to bed at the same time and I get more sleep, if he goes to bed earlier chances are I will not go to bed at the same time and have to get up earlier to feed him as he still gets up at least once a night to eat.)

Thoughts? When did you all put your 2 month old to bed? And when did you start an actual bedtime? When are they old enough for that?

Thanks mamas!