It’s time for fun with punctuation again!
I would put a period after “sing.” I would have her try and get someone to sing with her. Laertes. Gertrude. Claudius. Someone. And then begin the song with “a-down a-down An you call him a-down-a.”
Which is a pretty odd song by the way. Especially since the last part of it, depending on the accent, can sound like she’s calling someone a downer….which was probably not a thing in the 1600s but is hard not to hear in the 2000s.