Can I install a 60A main breaker in a load center rated for 125A?
Yes you can get a 60A main breaker for this panel

Your panel uses what is known as a QOM1 main breaker frame size -- this is standard for Square-D panels up to 125A.  While an ordinary Homeline 60A breaker won't fit there, the good news is that Square-D does make a QOM60VH -- so simply install that into your panel as per the supplied instructions, and you'll be golden as far as your main breaker goes. (Some other panel makes would require you to use Harper's approach of using a backfed branch breaker for the main, instead.)

You'll also need a PK15GTAL ground bar or two, as this will be a subpanel instead of a main panel.