Hi Alison, regret to tell you that there is no way can a restore be made directly from v1.9 to v2.7. The security structures of both version are very different but more importantly, the databases are so very different that the is few similarities, apart from names. Perhaps most important is that the way in which backup files are created and then restored uses different methodologies. However, this is not hopeless.
If you have in your backups somewhere a v2.2, or if you can download a v2.2 from the Moodle.org, found on this page, install it somewhere other than your server, restore the v1.9 file then back it up again for the v2.7. That is currently the only way I know it can be done.
Having said that, it is not always a straight forward operation either. If the v1.9 file has references to blocks or other plugins not used in a v2.2, for example, it may not restore properly. To get around that, unzip the original file, open the moodle.xml file in a test file editor other than Notepad, look for references to blocks and remove them. Keep the command tags, but remove the data contained within. Save the file, re-zip it then try again. This might take several attempts, but I often found that it was easier to do this than to rebuild the course itself.
Good luck.
EDIT: Thinking about it... the zip file should contain the images used in the course, so if what is above is too daunting, best bet is to look for the text used in the course after unzipping the file, and opening the moodle.xml file, copy and paste it, then use that to rebuild the course. There is a lot of corrective editing, which makes the above actually faster. I have done this too, so whichever suits you best.