Tabla dinámica de SQL Server con agregados de varias columnas

Haría esto ligeramente diferente aplicando tanto el UNPIVOT y el PIVOT funciones para obtener el resultado final. El despivote toma los valores tanto del totalcount y totalamount columnas y las coloca en una columna con varias filas. Luego puede pivotar sobre esos resultados.:

select chardate,
  Australia_totalcount as [Australia # of Transactions], 
  Australia_totalamount as [Australia Total $ Amount],
  Austria_totalcount as [Austria # of Transactions], 
  Austria_totalamount as [Austria Total $ Amount]
from
(
  select 
    numericmonth, 
    chardate,
    country +'_'+col col, 
    value
  from
  (
    select numericmonth, 
      country, 
      chardate,
      cast(totalcount as numeric(10, 2)) totalcount,
      cast(totalamount as numeric(10, 2)) totalamount
    from mytransactions
  ) src
  unpivot
  (
    value
    for col in (totalcount, totalamount)
  ) unpiv
) s
pivot
(
  sum(value)
  for col in (Australia_totalcount, Australia_totalamount,
              Austria_totalcount, Austria_totalamount)
) piv
order by numericmonth

Consulte SQL Fiddle con demostración.

Si tiene un número desconocido de country nombres, entonces puede usar SQL dinámico:

DECLARE @cols AS NVARCHAR(MAX),
    @colsName AS NVARCHAR(MAX),
    @query  AS NVARCHAR(MAX)

select @cols = STUFF((SELECT distinct ',' + QUOTENAME(country +'_'+c.col) 
                      from mytransactions
                      cross apply 
                      (
                        select 'TotalCount' col
                        union all
                        select 'TotalAmount'
                      ) c
            FOR XML PATH(''), TYPE
            ).value('.', 'NVARCHAR(MAX)') 
        ,1,1,'')

select @colsName 
    = STUFF((SELECT distinct ', ' + QUOTENAME(country +'_'+c.col) 
               +' as ['
               + country + case when c.col = 'TotalCount' then ' # of Transactions]' else 'Total $ Amount]' end
             from mytransactions
             cross apply 
             (
                select 'TotalCount' col
                union all
                select 'TotalAmount'
             ) c
            FOR XML PATH(''), TYPE
            ).value('.', 'NVARCHAR(MAX)') 
        ,1,1,'')

set @query 
  = 'SELECT chardate, ' + @colsName + ' 
     from 
     (
      select 
        numericmonth, 
        chardate,
        country +''_''+col col, 
        value
      from
      (
        select numericmonth, 
          country, 
          chardate,
          cast(totalcount as numeric(10, 2)) totalcount,
          cast(totalamount as numeric(10, 2)) totalamount
        from mytransactions
      ) src
      unpivot
      (
        value
        for col in (totalcount, totalamount)
      ) unpiv
     ) s
     pivot 
     (
       sum(value)
       for col in (' + @cols + ')
     ) p 
     order by numericmonth'

execute(@query)

Ver SQL Fiddle con demostración

Ambos dan el resultado:

|             CHARDATE | AUSTRALIA # OF TRANSACTIONS | AUSTRALIA TOTAL $ AMOUNT | AUSTRIA # OF TRANSACTIONS | AUSTRIA TOTAL $ AMOUNT |
--------------------------------------------------------------------------------------------------------------------------------------
| Jul-12               |                          36 |                   699.96 |                        11 |                 257.82 |
| Aug-12               |                          44 |                  1368.71 |                         5 |                 126.55 |
| Sep-12               |                          52 |                  1161.33 |                         7 |                  92.11 |
| Oct-12               |                          50 |                  1099.84 |                        12 |                 103.56 |
| Nov-12               |                          38 |                  1078.94 |                        21 |                 377.68 |
| Dec-12               |                          63 |                  1668.23 |                         3 |                  14.35 |