How to get list of 0 and 1 status from group of zero and 1 list in sql

Seems like a classic Islands and Gaps problem with edges.
Try this:

with changes as (
    select  status - lag(status,1,0) over (order by timestamp) change
           ,timestamp
    from    Table1
    )
,up as (
    select  timestamp
           ,row_number() over (order by timestamp) rn
    from    changes
    where   change = 1
    )
,down as (
    select  timestamp
           ,row_number() over (order by timestamp) rn
    from    changes
    where   change = -1
    )
select  u.timestamp up,d.timestamp down,u.rn rn
from    up u
join    down d on u.rn = d.rn
order by rn

Here's[^] the fiddle.
This works on SQLServer 2012 and Oracle 10G, but earlier versions lack the Lag function. It can be implemented on those easy enough using rownumber and a self join.
So if you have an earlier version or another database you'll need to update your question with database and version.

Here's an updated solution for MySQL:

SELECT  up.TIMESTAMP up,down.TIMESTAMP down,up.rn
FROM    (
    SELECT  TIMESTAMP
        ,@r1 := @r1 + 1 AS rn
    FROM    (
        SELECT  t1.timestamp
        FROM    Table1 t1 
        left OUTER JOIN Table1 t2 ON t1.timestamp = t2.timestamp + 1
        WHERE   t1.status - ifnull(t2.status,0) = 1
        ORDER BY t1.timestamp
        ) t1
        ,(SELECT @r1 := 0) r
    ) up
    ,(
        SELECT  TIMESTAMP
        ,@r2 := @r2 + 1 AS rn
    FROM    (
        SELECT  t1.timestamp
        FROM    Table1 t1 
        left OUTER JOIN Table1 t2 ON t1.timestamp = t2.timestamp + 1
        WHERE   t1.status - ifnull(t2.status,0) = -1
        ORDER BY t1.timestamp
        ) t1
        ,(SELECT @r2 := 0) r
    ) down
WHERE   up.rn = down.rn
ORDER BY up.rn

Here's[^] the fiddle.
When you need to create a contraption like this it's a fitting time to say how much I despise MySQL.

Note: This code assumes that there are no gaps in the timestamp sequence.
If there are, you need to add a couple more IfNull