I think using SQL Profiler here is overkill in this situation, particularly as it can create a substantial load on the server depending on what you trace. SQL Server exposes the raw values used for its performance counters via the sysperfinfo system table; you should just be able to run this query once each day and subtract the values to work out how many SQL requests you received for the day:
SELECT cntr_value
FROM sysperfinfo
WHERE object_name = 'SQLServer:SQL Statistics'
AND counter_name = 'Batch Requests/sec'
This will obviously only work if the server is up for the whole day; restarting will reset the number.