In addition to word studies and lexicons, how a word is used conveys meaning.
In this case the word “doubt” ἐδίστασαν is used only twice in the New Testament:
So he said, “Come.” Peter got out of the boat, walked on the water, and came toward Jesus. But when he saw the strong wind he became afraid. And starting to sink, he cried out, “Lord, save me!” Immediately Jesus reached out his hand and caught him, saying to him, “You of little faith, why did you doubt ἐδίστασας?” (Matthew 14:29-31 NET)
As seen from the event doubt does not mean unbelief. Peter believed and so he got out of the boat. Then he doubted.
The HELPS Word-studies states:
the word comes from dis “two or double” and stasis “stance or standing” – properly, going two ways, shifting between positions; choosing “a double stance” and hence vacillate (waiver); (figuratively) uncertain at a crossroad because refusing to choose one way over the other – “wanting to have our cake and eat it too”, to halt between two opinions (view, beliefs) [distazo]
In Peter’s case, he got out of the boat, started to go toward Jesus and then something happened. According to Jesus Peter “ἐδίστασας.”
One can imagine Peter walking on water toward Jesus and with each step moving further away from the boat. If Peter continues to move toward Jesus he will reach a crossroad where he must reaffirm (or question) his decision. Should he continue to move toward Jesus or go back to the boat? At first Peter will be close enough to the boat to go back; at some point Peter must choose to continue to move beyond the safety of going back to the boat.
Peter waivered: he vacillated refusing to choose one way over the other. He did not go back to the boat (a form of unbelief); yet he did not continue moving toward Jesus (a form of doubt).
The expectation a Jewish person had about the future was that God would gather all of the Jewish people back to a restored kingdom of Israel:
The LORD will then be king over all the earth. In that day the LORD will be seen as one with a single name. All the land will change and become like the Arabah from Geba to Rimmon, south of Jerusalem; and Jerusalem will be raised up and will stay in its own place from the Benjamin Gate to the site of the First Gate and on to the Corner Gate, and from the Tower of Hananel to the royal winepresses. And people will settle there, and there will no longer be the threat of divine extermination—Jerusalem will dwell in security. (Zechariah 14:9-11 NET)
After restoring Israel, the world will then come to Jerusalem to worship the King, the LORD who rules over all the earth. In particular, each year all nations are expected to come to Jerusalem to worship at the time of the Feast of Tabernacles:
Then all who survive from all the nations that came to attack Jerusalem will go up annually to worship the King, the LORD who rules over all, and to observe the Feast of Temporary Shelters. But if any of the nations anywhere on earth refuse to go up to Jerusalem to worship the King, the LORD who rules over all, they will get no rain. (Zechariah 14:16-18 NET)
After the resurrection the disciples continued to hold on to this expectation:
So when they had gathered together, they began to ask him, “Lord, is this the time when you are restoring the kingdom to Israel?” (Acts 1:6 NET)
Matthew records Jesus instructing the disciples what to do next:
Therefore go and make disciples of all nations, baptizing them in the name of the Father and the Son and the Holy Spirit, teaching them to obey everything I have commanded you. And remember, I am with you always, to the end of the age.” (Matthew 28:19-20 NET)
The Christian understanding that the disciples were to "go" as in leave Israel to make disciples of all the earth is completely opposite of the Jewish expectation that all nations will come to Jerusalem. The Old Testament belief is such that the restoration of Israel leads to the world knowing the one true God by coming to Jerusalem and worshiping Him at the time of the Feast of Tabernacles not by the LORD's disciples leaving Israel to go and teach the nations.
So what did those disciples who worshiped Jesus on the mountain do?
According to Acts they left the mountain and returned to Jerusalem and after receiving the Holy Spirit on the day of Shavuot, they remained in Jerusalem. They stayed on after the Feast of Tabernacles.
They all doubted; they all waivered; they all remained in Jerusalem. They did not "go." Eventually circumstances would force a different decision but after worshiping on the mountain and returning to Jerusalem they wavered between how to understand the command to go and make disciples of all nations.