Peggy and Mike's version is from Ruth Crawford Seeger's American Folk Songs for Children (Doubleday, 1948, pp. 72-75; with music):

JIM ALONG JOSIE
(OKLAHOMA)

1. Hey jim along, jim along Josie,
Hey jim along, jim along Jo.
Hey jim along, jim along Josie,
Hey jim along, jim along Jo.

2. Walk jim along, jim along Josie,
Walk jim along, jim along Jo. (Repeat)

3. Hop jim along, jim along Josie,
Hop jim along, jim along Jo.

IMPROVISATION and RHYTHMIC PLAY: Josie may have thoughts or motions other than those in the traditional yext given above.

4. Run, jim along, jim along Josie, etc.
5. Jump, jim along, jim along Josie, etc.
6. Tiptoe along, jim along Josie, etc.
7. Crawl along, jim along, jim along Josie, etc.
8. Swing along, sing along, jim along Josie, etc.
9. Roll, jim along, jim along Josie, etc.

An invitation is sometimes appreciated:

Let's go walking, jim along Josie, etc.
Let's go running, jim along Josie, etc.
Let's sit down now, jim along Josie, etc.

For rhythmic play the music should be repeated many times without stopping. The words will probably be sung only once, or not at all.

ACCOMPANIMENT: Speed and type of accompaniment may be adapted to the various rhythmic activities. The sample variations which follow are suggestions only. Do not use them if you can make your own. In all of them the chordal basis is the same.
The simple dance-song Jim Along Josie is said to be based on an old minstrel song. It is widely known, especially as a game or play-party song. In some versions Josie appears to be the dance itself:

Hold my mule while I dance Josie.

In a very old one, still sung, "Josie" is something to wear:

Who's been here since I been gone?
Pretty little girl with a josey on.

"Hey jim along" is also sung "Hey get along," "Hi come along," "Hey jam along," "Come-a-get along," "Come-a-high, jim along."

~Masato