Join query

Hi,
I have two tables: establishment which contains these columns: id, name,
longitude, latitude, geom (Geometric column)
Product contains: id, name, establishment_id
First of all I want to select the establishment within a radius.
I run this query:
select e.name, e1.name
from establishment as e, establishment as e1
where e.id <> e1.id
and e1.id = 1
and ST_DWithin(geom, ST_MakePoint(e1.longitude, e1.latitude)::geography,
1000)

The result of this query returns all the establishment within a radius 1KM
from from a given establishment which has an id = 1.

After that I want to get the product's name of each establishment from the
query's result.

Is there an other optimized solution to make a query such this:
select * from (
select e.name, e1.name, e.id
from establishment as e, establishment as e1
where e.id <> e1.id
and e1.id = 1
and ST_DWithin(geom, ST_MakePoint(e1.longitude, e1.latitude)::geography,
1000)) as tmp inner join product as p on p.establishment_id = tmp.id