You can buy tickets for Rundertaarn (Round Tower) in advance online or buy them at the door when you arrive.
Rundetaarn is surprisingly stroller-friendly, as there are no steps but a spiral ramp in the middle of the round tower that goes almost all the way to the top. To go outside on the round observation deck up top (for amazing views!), you'll need to leave the stroller below.
Rundetaarn admission is included in the Copenhagen Card.