No.
As indicated by the Sage Advice Compendium (2017):
Can you use dispel magic on the creations of a spell like animate dead or affect those creations with antimagic field?
Whenever you wonder whether a spell’s effects can be dispelled or
suspended, you need to answer one question: is the spell’s duration
instantaneous? If the answer is yes, there is nothing to dispel or suspend.
So, yes, duration is entirely relevant.
The entry goes on to detail why it functions this way, to paraphrase though: the effect that animates the dead is instantaneously brought into being by magic, but is not continuously sustained by magic afterwards. Therefore, skeletons can enter an antimagic field at their leisure and hack you to bits.
Of note: Danse macabre has a duration on the spell and therefore you could dispel one of the animated creatures.
Just for fun, if dispel magic worked in this way it would be the most powerful spell in the game and here is why:
Anyone that has ever been the target of a cure wounds (or for that matter revivify, raise dead, reincarnation, resurrection, etc.) spell could potentially die outright if targeted by dispel magic since it would erase all previous curative effects in an instant.
No, it does not.
The Dispel Magic description says:
Choose one object, creature, or magic effect within range. Any spell of 3rd level or lower on the target ends.
And Animate Dead has a duration of:
Duration: Instantaneous
So there is no spell effect to dispel as Animate Dead has a duration of instantaneous, so as Dispel Magic only works on a spell it has nothing to work on and does nothing. Also clearly stated here stated in this Sage Advice:
Can you use dispel magic on the creations of a spell like animate dead or affect those creations with antimagic field? Whenever you wonder whether a spell’s effects can be dispelled or suspended, you need to answer one question: is the spell’s duration instantaneous? If the answer is yes, there is nothing to dispel or suspend.
The control of the undead granted by the spell is a consequence of the spell being cast, not an on-going magical spell, in the same sense as the fires started by a fireball are an on-going non-magical effect. The zombies are strictly loyal to the caster for a period of time, bonded to them like ducklings are to their mother, and in the same way the fires and damage from a fireball last for a period of time and cannot be dispelled, neither can this bond.
Best Answer
The SRD says: "The GM makes one roll for an entire group of identical creatures, so each member of the group acts at the same time."
Note: the casting time for Animate Dead is 1 minute, so it's unlikely to occur during combat. But if it could, you might use the precedence from the many Conjure spells (like Conjure Animals), which say "Roll initiative for the summoned creatures as a group, which has its own turns".
Personal experience: despite the above, every group I've played with found it intuitive/easy to just handle these things on the caster's turn as a home rule.