It may be driver related, even though most modern readers do not require special driver installations.
Its very odd that it wants to map this to Q: unless you have many other drives before it from C: to P:
I understand drive Q is something created by Microsoft office
Microsoft Office does not create drives. Drives are mounted by the Operating Systems Disk Management System. You should be able to go to Disk Management and reassign this to a different available letter. (If the system wants to format the card, say no or it will wipe your data... sometimes Windows on the rare occasion detects new disks/cards and states it needs to be formatted even though its already formatted and contains data.)
The card reader works fine on other computers
Are these computers Windows or a different OS? If they are Windows are they also Windows 7 or different OS. Please add more info as to what this drive works fine on.
Do you know what format the card was formatted in?