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In addition to using explorer view, as it was already answered.

This is basically the question on how to copy a form library with its content which is easily searchable.

In the same site collection, in Form Library Settings I would have used "Save Form Library as template" having checked "Include Content". This template choice will appear for creation of new form libraries.

For copying a form library to another site collection, it is also possible to save the created template as STP file.

You can find a few more methods like granular backup-restore, engagement of Sharepoint 2010 Management Shell (Export-SPWeb / Import-Spweb)m etc.

Update:
Note that moving Infopath XML data forms is unrelated to republishing an Infopath XSN form template or location of Infopath form template (here is about changing published location of a template).
If you copy the Infopath XML form data , they still will reference the same template.
If you deleted a library, you can restore it from Recycle Bin.

This is in Sharepoint 2010. Sorry, I never worked with 2007, have no idea (and access to see) how it is there and I missed that the question was about 2007.

In addition to using explorer view, as it was already answered.

This is basically the question on how to copy a form library with its content which is easily searchable.

In the same site collection, in Form Library Settings I would have used "Save Form Library as template" having checked "Include Content". This template choice will appear for creation of new form libraries.

For copying a form library to another site collection, it is also possible to save the created template as STP file.

You can find a few more methods like granular backup-restore, engagement of Sharepoint 2010 Management Shell (Export-SPWeb / Import-Spweb)m etc.

Update:
Note that moving Infopath XML data forms is unrelated to republishing an Infopath XSN form template or location of Infopath form template (here is about changing published location of a template).
If you copy the Infopath XML form data , they still will reference the same template.
If you deleted a library, you can restore it from Recycle Bin.

This is in Sharepoint 2010. Sorry, I never worked with 2007, have no idea (and access to see) how it is there and I missed that the question was about 2007.

In addition to using explorer view, as it was already answered.

This is basically the question on how to copy a form library with its content which is easily searchable.

In the same site collection, in Form Library Settings I would have used "Save Form Library as template" having checked "Include Content". This template choice will appear for creation of new form libraries.

For copying a form library to another site collection, it is also possible to save the created template as STP file.

You can find a few more methods like granular backup-restore, engagement of Sharepoint 2010 Management Shell (Export-SPWeb / Import-Spweb)m etc.

Update:
Note that moving Infopath XML data forms is unrelated to republishing an Infopath XSN form template or location of Infopath form template (here is about changing published location of a template).
If you copy the Infopath XML form data , they still will reference the same template.
If you deleted a library, you can restore it from Recycle Bin.

This is in Sharepoint 2010. Sorry, I never worked with 2007, have no idea (and access to see) how it is there and I missed that the question was about 2007.

In addition to using explorer view, as it was already answered.

This is basically the question on how to copy a form library with its content which is easily searchable.

In the same site collection, in Form Library Settings I would have used "Save Form Library as template" having checked "Include Content". This template choice will appear for creation of new form libraries.

For copying a form library to another site collection, it is also possible to save the created template as STP file.

You can find a few more methods like granular backup-restore, engagement of Sharepoint 2010 Management Shell (Export-SPWeb / Import-Spweb)m etc.

Update:
Note that moving Infopath XML data forms is unrelated to republishing an Infopath XSN form template or location of Infopath form template (here is about changing published location of a template).
If you copy the Infopath XML form data , they still will reference the same template.
If you deleted a library, you can restore it from Recycle Bin.

This is in Sharepoint 2010. Sorry, I never worked with 2007, have no idea (and access to see) how it is there and I missed that the question was about 2007.

In addition to using explorer view, as it was already answered.

This is basically the question on how to copy a form library with its content which is easily searchable.

In the same site collection, in Form Library Settings I would have used "Save Form Library as template" having checked "Include Content". This template choice will appear for creation of new form libraries.

For copying a form library to another site collection, it is also possible to save the created template as STP file.

You can find a few more methods like granular backup-restore, engagement of Sharepoint 2010 Management Shell (Export-SPWeb / Import-Spweb)m etc.

Update:
Note that moving Infopath XML data forms is unrelated to republishing an Infopath XSN form template or location of Infopath form template about changing published location of a template.
If you copy them, they still will reference the same template.
If you deleted a library, you can restore it from Recycle Bin.

This in Sharepoint 2010. Sorry, I never worked with 2007 and I missed that it is about 2007.

In addition to using explorer view, as it was already answered.

This is basically the question on how to copy a form library with its content which is easily searchable.

In the same site collection, in Form Library Settings I would have used "Save Form Library as template" having checked "Include Content". This template choice will appear for creation of new form libraries.

For copying a form library to another site collection, it is also possible to save the created template as STP file.

You can find a few more methods like granular backup-restore, engagement of Sharepoint 2010 Management Shell (Export-SPWeb / Import-Spweb)m etc.

Update:
Note that moving Infopath XML data forms is unrelated to republishing an Infopath XSN form template or location of Infopath form template (here is about changing published location of a template).
If you copy the Infopath XML form data , they still will reference the same template.
If you deleted a library, you can restore it from Recycle Bin.

This is in Sharepoint 2010. Sorry, I never worked with 2007, have no idea (and access to see) how it is there and I missed that the question was about 2007.