Not by RAW
Simply because the rules written, which you have quoted, say nothing about it being such. It doesn’t mention Leadership or Leadership’s cohort at all, and while it mentions similarities between Wild Cohort and Animal Companion, it does not actually state that Wild Cohort is or counts as Animal Companion.
It’s more than reasonable to houserule it, though
Allowing someone to qualify as having an Animal Companion or Cohort, because they have the Wild Cohort feat, is perfectly reasonable. I have done so in many games, and it’s never been an issue.
In this case, though, I would not actually state any interaction between these things. If you are a druid or ranger and take Wild Cohort, you just get both an Animal Companion and a Wild Cohort, as separate creatures. Same, too, if you take Wild Cohort as well as Leadership: you get a regular cohort as well as the wild one. The two don’t interact with one another.
The Ranger's companion is ...
... is trained to
fight alongside you.
It is not trained as a mount. And ...
The beast obeys your commands as best as it can. It
takes its turn on your initiative, though it doesn’t take an
action unless you command it to. On your turn, you can
verbally command the beast where to move (no action
required by you). You can use your action to verbally
command it to take the Attack, Dash, Disengage, Dodge,
or Help action.
The rules are quite specific here; you do not need to use your action to command your companion to Cast a Spell, Hide, Ready, Search or Use an Object. Now some of these are not very useful but Ready has definite possibilities - "Ready to attack the first creature that attacks me" for example.
Moving on to what a mount can do.
While you're mounted, you have two options. You
can either control the mount or allow it to act independently. Intelligent creatures, such as dragons,
act independently.
You can control a mount only if it has been trained
to accept a rider. Domesticated horses, donkeys, and
similar creatures are assumed to have such training.
If your companion is intelligent (unlikely) it will always act independently. If it has not been trained to take a rider (likely) it will always act independently. If it acts independently it is subject to the rules of the companion. If you command it, it will cost you your action is on the companion list of actions. If you don't command it, it acts as the DM sees fit.
If it is both unintelligent and trained to take a rider (like a horse) it must follow the rules for both a mount and a companion. If it is controlled, it can Dash, Disengage and Dodge at the cost of your action
The three options that any other mount gets for free (Dash, Disengage and Dodge) cost your action. So a companion horse is worse than a regular horse. Now, feel free to stop and call "stupid" but that would be a house rule.
Best Answer
You can't.
The enhancement at level 11 adds the celestial creature simple template and "becomes a magical beast for the purposes of determining which spells affect it."
The Monstrous Mount feat can give you something a little cooler than this, but of the mounts listed, unicorn is not one. The options listed there are:
Monstrous Companion also gives you access to a companion which is monstrous, but again unicorn is not listed there.
Leadership can grant you a cohort in addition to your animal companion, but doesn't modify your divine bond class feature .
This does not mean you can pick a celestial creature or magical beast, only that the bond you already have (since level 5 when you chose to take a steed) becomes a magical beast.
Without GM fiat, there is no way to gain a unicorn as your divine bond mount (and I think most unicorns would be quite offended by the notion that they are mere beasts of burden, to be mounted and ridden upon by men, for noble purposes or otherwise!).