If you haven't already, I'd recommend taking a look at the Unearthed Arcana that discusses feat-building. I'm not a fan of the feats in that particular article myself, but I do appreciate what it has to say on the design philosophy of feats.
That said, let's tackle your feat from a different perspective. As mentioned, determining balance just by looking at similar feats is difficult, given that there are no other class-specific feats. There are, however, a number of feats that mimic or expand on class features, and vice versa. Since your suggested feat would do something similar, we can limit ourselves to just those feats and features for comparison. Of these, the most directly comparable is the Martial Adept feat, and the feat that invites the most scrutiny is the Ritual Caster feat.
The Martial Adept feat straight up gives you a weaker version of the Battle Master archetype's Combat Superiority feature if you don't already have it, and gives you the equivalent of a level improvement if you do already have it (the abilities gained by Martial Adept are, for a Battle Master, exactly identical to what they would receive at 7th and 15th level). Were your feat trying to do exactly the same thing, we could therefore say that, if it wanted to be balanced with this feat, it would need to lose the prerequisite you've attached. It should instead provide anyone who takes it with the ability to pick up a warlock feature, and if a warlock takes it, it should increase the power of a feature they would already have.
Should that feature be a single invocation? Tough question. Invocations are certainly one of the hallmarks of being a warlock, along with the rapid-recharge spell slots and the "daddy issues" that come from having a patron. More importantly, if you wanted to mimic the Martial Adept feat and grant a weaker version of an archetype feature, you would need to make a feat that grants a patron boon, which creates far more problems than it would solve. The two safest bets to grant from the warlock features is an invocation or a fast-recharge spell slot.
Something else to consider, which has already been pointed out, is that granting even a single invocation can be unbalanced- the more powerful invocations are far nastier than any feat, the weaker ones could be equivalent to less than half a feat, and in between we have invocations such as the Book of Secrets, which is a more powerful version of an already extant feat, Ritual Caster. What should be done about this?
A not insignificant number of feats invite powerful combinations- my personal favorite is combining Eldritch Spear with Spell Sniper to give me an at-will attack with multiple shots, a range of 600 feet and no disadvantage for range or partial cover. Doing so requires that I pick a particular combination of cantrip, invocation and feat, and thus I pay an opportunity cost for it. The same applies to using a feat that provides you with an extra invocation to pick out a stronger version of another feat- in order to do so, the character in question would have to satisfy the prerequisites, meaning that only warlocks with the Pact of the Tome could have it.
SO: To summarize this section, I think that a feat granting an invocation would work, but the prerequisite is unnecessary and, if you're looking to balance your feat against the PHB feats, undesirable.
Next, the other parts of the feat- the +1 bonus to Charisma and the extra cantrip.
I just mentioned Spell Sniper, so let's look at it real quick. It provides one of a limited range of cantrips, and two other features besides, one of which is similar to (and as mentioned, stacks with) an invocation. Would it be reasonable to allow you to have a similar set of features?
I don't think so. A +1 bonus to an ability score is widely considered to be the equivalent of half a feat, and given that we recently established that an invocation is more or less balanced against a single feat (or rather, the imbalance present averages out to a single feat), there's no way to justify adding it here. It would be similar to writing a new feat called "Martial-er Adept," which gives you everything Martial Adept does, plus a +1 bonus to Strength.
What about the cantrip? Again, tough call. I would prefer to split the difference. Feats that limit the options for a cantrip also provide more features, signifying that the lack of choice lowers the value of the cantrip when it comes to feat-building. Considering Magic Initiate and Spell Sniper, we can consider a cantrip to be worth about 1/3 of a feat- and considering that an invocation is basically a feat unto itself, the best bet to keep this feat balanced is to limit the cantrip as much as possible.
My suggestion, then, for your feat would be:
Feat: Eldritch Adept
You learn the eldritch blast cantrip, if you don't already know it. Your spellcasting ability for this cantrip is Charisma. In addition, you learn one eldritch invocation of your choice. If the eldritch invocation has any prerequisites, you must meet them to learn it. You can learn the invocation at the same time that you meet the prerequisites.