When using Vi Peacekeeper, when Vi attacks an enemy unit she will stun it and if it dies Vi will proceed to the next unit. My question is does she also stun the next unit?

No, Vi, Peacekeeper does not stun a second unit if the first one she targets dies.

According to her card text, her ability is: "When I attack, [Stun] an enemy unit here."

Here is the breakdown of why she only stuns one unit:

1. Trigger Condition: Her ability is an "Attack Trigger" (Rule 383.4.e). It triggers exactly once, at the moment she gains the "Attacker" designation during combat.
2. Single Effect: The ability contains one instruction to "[Stun] an enemy unit." When that ability resolves, it carries out that instruction by stunning one unit.
3. No "Repeat" or "Extra": Her ability does not include the keyword "Repeat" or any instruction to look for another target if the first one is killed.
4. "Next Unit" Misconception: While Vi may be a powerful attacker, the game rules do not automatically allow an attacking unit to "proceed" to another unit and trigger its attack ability again just because the first target died. Once her "When I attack" ability resolves, it is finished for that combat.

If you are seeing Vi defeat multiple units in combat, it is likely due to her high Might (5) allowing her to win combat against the next unit she faces during the Combat Damage Step, not because she is re-triggering her stun ability.