"Jim along" most likely means "get along".

Notes

You can include verses with other actions, like "crawl", "skip", etc.

2nd Version:

Hey Jim along,
Jim along Josie,
Hey Jim along,
Jim along Jo.

Hey walk along,
Walk along Josie,
Hey walk along,
Walk along Jo.

Hey hop along,
Hop along Josie,
Hey hop along,
Hop along Jo.

You can add verses with other actions: Run, spin, crawl, etc...

Game Instructions

Follow the action that you're singing about in each verse while going around in a circle. i.e. Walk around in a circle, hop around in a circle, run around in a circle, etc.

Listen
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In the video below you can hear the 2nd version that's in the Song Notes...

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Sheet Music

Sheet Music - Jim Along Josie