EU national (Lithuanian) in UK -- regarding Dominican fiancée's immigration.

[Tsayahada]

Hello,

First of all, thank you for this forum.

Also, just wanted to say that it is very weird that the search bar disappeared once I logged in and not sure if intentional so just wanted you guys to know.

Sorry if this is a duplicating topic, but I did not find exactly the same thread anywhere and the FAQ pinned in this section did not answer me fully either.

I am willing to read stuff on my own, the only thing I would like help with is links to information or tips that touches my situation. We already read tons of stuff and sort of have an idea, but now we want to narrow down the information regarding our specific situation and if there are no hidden corners that we may be missing.

What we want to do is for my girlfriend to immigrate to UK. Information about us (sorry if some of the information feels unnecessary, but I'll provide everything just in case it may have significance):

About me
Age: 23.
Nationality: Lithuanian.
Residence: London, UK. Lived here for 4,5 months.
Education: IT Enginnering Bachelor (received in Lithuania).
Occupation: Junior Front End Web Developer, worked for 2 months.
Salary: £30000.

About her
Age: 20.
Nationality: Dominican.
Education: Finished school, working on University (not sure of the degree's rank in EU/UK standards)

The plan:
I would travel to Dominican Republic on 2018-08, marry her and stay there for an appropriate time so the marriage does not seem fabricated. Then she would apply for the EEA family permit, then we would travel to UK and try to get the UK residence card for her to stay or maybe get a student's permit if we decided for her to start studying right off the bat.

My doubts:
How much time should pass after marriage before she applies for EEA family permit?
How much of an influence Brexit will be on our plans?
Are there any other good ways to get her into UK besides the EEA family permit?
Any extra tips, keywords to google that I should know?

Thank you very much for your time and efforts.