Nope, not Joshua. Yes, of course, he was, but there’s another successor to Moses in dramatic ways. In the most recent fascicle of Journal for the Study of the Old Testament an article by Bruce Herzberg, at Bentley University in Waltham Mass, presents an excellent case for seeing Deborah as a successor to Moses. As he puts it, “far more similar than either traditional or modern commentators acknowledge.” ["Deborah and Moses," JSOT 38/1 (2013): 15-33.]
You can read up about Moses for this in Exodus 14-15 and about Deborah in Judges 4-5. Here is a sampling of his article and the major lines of similarities (and Herzberg marches out all the evidence in readable fashion):
1. Both defeat better-armed forces that are equipped with chariots.
2. Both victories are followed by a song, and the two songs are seen by many to be the earliest strata of the Old Testament.
3. These are the only pairings of a narrative poem with a prose narrative of the same event.
4. Both are connected to the Kenites, descendants of Moses’ father-in-law.
5. Deborah, like Moses, is described in the Bible in the act of judging.
6. Deborah, like Moses, is a prophet who speaks the Word of God to the people.
7. Moses judged in a tent, Deborah under a tree (location specified).
8. Deborah, like Moses, orders a military leader into action, presenting herself as the voice of God, but stays behind the troops at the top of a hill to inspire rather than fight.
9. In the battles of both chariots are disabled by a sudden rush of water.
10. Both Moses and Deborah sing victory songs.
The Medieval rabbis read Exodus 14-15 with Judges 4-5 in their lectionaries.
I find this information fascinating and clearly indicative of some parallels between Moses and Deborah, a (but not the only) successor to Moses.