Q:

Is there some way to request peer review on an edit? 

I just edited this answer, I just reached 2000+ reputation and the edit got immediately accepted.  Is there some way to turn this off? 
I´m fairly sure this was a good edit, but I have done bad edits before, like the one for this answer, where I removed all incorrect information, which was most of the answer.  That edit was correctly rejecte by peer review, because "This edit deviates from the original intent of the post.  Even edits that must make drastic changes should strive to preserve the goals of the post's owner." 
I learned from that and will try to avoid doing something like that again, this is not possible without peer review, I felt unsure about that edit, but didn´t know about that reason to reject it and thought it would be fine, because I only removed incorrect information. 
I usually feel fairly sure about my edits, but there are some cases where I am unsure and where I would prefer to have someone else approve it via peer review. 
Is there a feature like that?  If not, then I would like to suggest such a feature.  It could work similar to how the "community wiki" checkbox works, then I could tick a checkbox that sends the edit to the review queue, rather than being imidiately accepted, whenever I feel unsure about an edit, or simply don´t want to make a final decision, I´m not perfect, I make mistakes. 
Adding a feature like that would make it possible to learn from mistakes, even at higher reputation levels.  In my case I feel like it´s too early to ALWAYS have the edit accepted without peer review, because I´m still learning and I reached this much reputation too quickly to fully understand the rules.  I´m bound to make mistakes and I don´t want anyone else to suffer for it. 
I do feel confident enough to decide when an edit feels a bit risky though, so I think simply having the option to have an edit peer reviewed would be enough. 
Alternatively I could just never make any edits if I´m not completely sure if they are good, but in that case I would no longer have the opportunity to learn if an edit is good, or not, so a lot of future edits that would be good would never be made, because I was unsure. 

A:

You can't suggest reviews anymore now that you've reached 2000 reputation.  The system (and the users who voted for your posts) trusts you to have learned how editing works by now, by having your suggested edits approved or rejected, and by seeing the edits of other users who have earned the same privilege as you. 
And frankly, the system seems to be working as expected!  You've noticed that some of your edits were rejected, and have learned why.  But as everyone knows, with great power comes great responsibility.  Now that you can edit posts without having your changes approved by other users, you should only make edits that you're feeling confident about. 
Similar feature requests have popped up from time to time on Meta Stack Exchange, like here.  It doesn't look like revoking your own privileges is going to be implemented. 

A:

Wrigglenite's answer covers the feature request side of things so I'll just address the act of editing itself:

Is there some way to request peer review on an edit? 

You already are!...kinda.  Every edit you make bumps that question to the front page, complete with a little 'modified by <UserName>' message and link that takes users directly to the post you edited.  So in a way, your edits are still pushed up to be reviewed by the community.  All that's changed is that we trust you enough to make those edits immediately, instead of first holding them back for community review. 

I´m still learning and I reached this much reputation too quickly to fully understand the rules.  I´m bound to make mistakes and I don´t want anyone else to suffer for it. 

You'll be fine.  It may seem daunting, but don't fret - edits are important, but are fairly trivial to change, update, or roll back - there's not a whole lot that can go terribly wrong.  If it helps, the Help Center gives some general guidance:

When should I edit posts? 
Any time you feel you can make the post better, and are inclined to do so.  Editing is encouraged! 
Some common reasons to edit are:

to fix grammatical or spelling mistakes
to clarify the meaning of a post without changing it
to correct minor mistakes or add addendums / updates as the post ages
to add related resources or hyperlinks

Tiny, trivial edits are discouraged - try to make the post significantly better when you edit, correcting all problems that you observe. 

If you feel it's a good edit, go ahead and make the judgement call.  If you miss something, or introduce a typo etc, someone else will just edit it again, or (worst case) roll it back.  You can see all your revisions on your profile (here), so if you want to check back a day or two later and see if anything changed, you can.