No that is not possible. Such Crash URLs are not publicly available,not even to the crash report submitter. (They could be used in correlation report generation or automated testing of those URLs)

In future if website addresses are important bookmark them or otherwise copy and record them. Had you used ordinary browsing you would have had access at least to the history information that would normally include such information (depending on your choice of settings)

• see also Private Browsing - Use Firefox without saving history

You appear to be using Firefox 16 ! you should update that is old insecure and unsupported.

• Update Firefox to the latest release

If you have problems with crashes other than on single specific faulty sites see

• Troubleshoot Firefox crashes (closing or quitting unexpectedly)

That is a disadvantage of running Firefox in Private Browsing mode that Firefox doesn't store or otherwise keep data from a Private Browsing mode session, so you lose all open tabs in case of a crash.
You would have to bookmark open tabs that you consider important especially if Firefox crashes often.

Note that Firefox 16.0.2 is the last version for OS X 10.5.x

• https://support.mozilla.org/kb/firefox-no-longer-works-mac-os-x-10-5

So your only option to keep using Firefox would be to update to OS X 10.6.8

Another option to consider is to install the last Firefox 10.0.x ESR version as that version is more recent than the Firefox 16.0.2 version.

• https://ftp.mozilla.org/pub/mozilla.org/firefox/releases/10.0.12esr/
• http://www.mozilla.org/en-US/firefox/10.0.12/system-requirements/