Maybe not the answer you are looking for if you are strict about doing this in QGIS, but I do these kind of conversions in PostgreSQL/PostGIS. It is easy to install if you don't have it and makes life much easier when dealing with geometry, at least for me.
First create schema data as you don't want to put your data in public schema:
CREATE SCHEMA data;
Then create the table:
CREATE TABLE data.table_name
(
id serial NOT NULL,
lat double precision,
lon double precision,
other_field text,
geom geometry(Point,26986),
CONSTRAINT table_name_pkey PRIMARY KEY (id)
)
You can include more fields according to your input file, just use correct types. Next step is to import the data into the table:
COPY data.table_name(lat,lon,other_field) FROM '/home/dejan/test.csv' DELIMITER ',' CSV HEADER;
Of course, use your fields and path. Use HEADER
if you have header in your input, like in my sample:
lat,lon,other_field
23,-79,test1
23.5,-79.5,test2
Create the geometry with desired EPSG:
UPDATE data.table_name set geom=ST_Transform(ST_SetSRID(ST_MakePoint(lon, lat),4326),26986);
And now you can convert to any EPSG available in PostGIS or custom added and export the coordinates:
select ST_X(geom) as long, ST_Y(geom) as lat, other_field from data.table_name;
pgAdmin can help you with some of these steps through graphical interface.