D.,
Although this is common among one year olds, they are old enough to learn it is not okay. This is a behavior that can't be ignored. At this age, you can start to put your son in time out for a minute or until he calms down, which ever takes longer.
He probably won't stay in place and if you hold him there he will probably like the attention, so find a cheap booster seat or stroller specifically for time out and strap him in. Don't stick around to calm him down. Leave him alone. It will take time because he is still little, but he will get the message within a couple of weeks, a month at most. Be consistent.
Best of luck,
S.
PS - I am also expecting baby #4 in May, also a girl. (We also had a girl, then two boys first.) Congrats to you!