Yes, this is OK
It's great that one of the kids wants to play their own character. The game should be fun for all players, and if one of them does not like his character and would like to play another one, and nobody objects, there is no issue.
If there are objections by other players, that is something to discuss outside of the game. Listen to what their concerns are and see if you can address them fairly. They may at some point in the future want to do the same thing, too.
It is no problem to create a new character that has the same level (and accumulated experience points) as the current character.
Official rules on starting equipment
The Dungeon Masters Guide has guidance on starting equipment (on page 38). Typically, the amount of wealth and magic items such a character would have would be lower than what a character of the same level can expect to earn by adventuring. If you all are happy with it, you can instead give the new character better starting equipment without problems.
This is a game. If everyone is fine with it, you can just replace the character, give them the equipment, and continue on. Everybody pretends the character was always like this and was always in the group and nothing happened.
This breaks internal continuity of the game world, and if you want to conserve it, you can instead play out the exchange of characters in game:
From an in-game perspective, the character leaving the adventure has earned his share of the treasure, and will want to keep it. Why should they hand this over to some newcomer they never met? You and your player will come up with a reason or back story.
For coins and generic equipment, it is easy, you can just give new ones to the new character, and the old character takes his with them. E.g. they both bought a longsword, they both happen to have a rope and backpack and so on.
Passing on magic items
It is trickier for magic items the old character found. First, are they the characters', or do they belong to the group and are just used by the character? If the group finds a magical longsword, that may be worth more than the character can afford to pay the others off for. If the sword belongs to the group and he leaves, he leaves it behind for the new character to take over. If the player wants to take over special items that are owned by the existing character, you have two options:
You give the new character another copy of the item. They could have a magical sword with the same technical stats and another backstory.
You and the player come up with a story why the current character would want to hand them over. Maybe they trade for an item the new character has and that the old one prefers.
Introducing the new character
You also should think about how that new character gets introduced to the group and earns their trust. Does the old character already know them, i.e. they are an old friend they happen to meet again? This makes it a lot easier. I had plenty of bungled up introductions of new characters, where the player wanted to show off their new character's cool powers but did nothing to earn the group's trust (in one case even ambushing them!), and it then was a painful exercise to come up with any reason why they would want him on the team.
A note on keeping treasure balance
If new characters introduced to the campaign bring their own wealth and items, and then also take over those of characters that leave, this will lead to an inflation of resources. We had that (although not in D&D), where each character that died had an heir that then joined the group bringing in new wealth...