From what I found, I have to agree with LegendaryDude.
According to the Divine Bond section of the Paladin page on D20pfrsd:
The second type of bond allows a paladin to gain the service of an unusually intelligent, strong, and loyal steed to serve her in her crusade against evil. This mount is usually a heavy horse (for a Medium paladin) or a pony (for a Small paladin), although more exotic mounts, such as a boar, camel, or dog are also suitable. This mount functions as a druid's animal companion, using the paladin's level as her effective druid level. Bonded mounts have an Intelligence of at least 6.
At 11th level, the mount gains the celestial creature simple template and becomes a magical beast for the purposes of determining which spells affect it.
Following the link to Animal Companion we can find this:
One of the surest ways to complicate the relationship between an adventurer and her animal companion is to cast awaken on the beast.
And for those of us who have yet to memorize all the spells (ex. myself):
An awakened animal gets 3d6 Intelligence, +1d3 Charisma, and +2 HD. Its type becomes magical beast (augmented animal). An awakened animal can't serve as an animal companion, familiar, or special mount.
Two final pieces of information are needed before we can begin our extrapolation: the "animal companions" accessible to a paladin of 11th level, and the stat block of a unicorn.
The list of "animal companions" available to a player with an effective druid level of 11 but is not an actual druid according to the Sample Animal Companion page is:
Badger, Bird, Camel, Constrictor Snake, Dog, Horse, Pony, Shark, Small Cat, Viper Snake, Viper Snake, Wolf
Presumably, you could select any of those animals as your mount, as long as you cloud justify it to your GM.
Yes, unicorn is not on that list, that is where the second piece of information ties in along with where I mentioned the awaken spell earlier.
(Blah blah blah)
Str 18, Dex 17, Con 16, Int 11, Wis 21, Cha 24
Okay, now for extrapolation.
What We Know
- The paladin's divine mount class feature functions similar to the druid's animal companion class feature.
- Upon reaching 11th level, the paladin's divine mount gains the Simple Celestial Template and is now counted as a Magical Beast for the purposes of determining which spells affect it.
- The possible "mounts" for a paladin of 11th level are Badger, Bird, Camel, Constrictor Snake, Dog, Horse, Pony, Shark, Small Cat, Viper Snake, Viper Snake, Wolf; as long as they can be justified to the GM.
What We Want to Know
Is it possible for a paladin to have a unicorn as it's divine mount through the effects of feats (such as Monstrous Mount, Monstrous Companion, and/or Leadership) and the effects gained at 11th paladin level.
RAW (Rules as Written)
Unicorn is not on the list of accessible companions to a paladin through any listing that I could find in an hour of searching.
RAE (Rules as Extrapolated)
The reason I brought up the awaken spell is that it contains a pretty important point. "An awakened animal can't serve as an animal companion, familiar, or special mount" because they are too intelligent to be considered a "regular beast." Having an awaken animal as your mount would be akin to having an Elf or Dwarf throw you on their shoulders and sprint through the land.
And for our purposes, technically a Unicorn would be considered to be an "awaken animal." It has an intelligence score of 11 (which is above average for humans) and a charisma score of 24 (which is heads and shoulders about most of the top tier influential people of any race [except goblin, but that's different]). Thus being awaken, it can't serve as a mount.
If one had a high enough leadership score (which for an 11th level paladin of all classes should be a piece of cake), you could possibly attract a unicorn as a cohort. Then, if your GM is feeling nice/lenient/bribed you could possibly be able to ride a unicorn then, but that is still doubtful.
Unless your GM specifically says you can, there are no rules that allow you to be this guy:
(Though if you're gun-slinging Catfolk paladin, you play paladins waaay differently than I have ever seen them played.)