You have a number of issues to research. Some are best asked about/researched in the FM Go Forum as that's the section for FM Go--the iPad/iPhone version of FileMaker. If you can set up reliable wireless connections (WiFi, 3G or 4G) a filemaker database can be hosted with Filemaker Pro or Filemaker server and your iOS users can connect to it in order to log items in and out of inventory.
I've seen several discussions of using barcode readers with such a device that indicate such an option can be made to work, but the implementation is not as simple as a scanner hooked directly up to a regular computer. I suggest searching out and reviewing posts on barcode scanning and Filemaker Go to learn more.
Then you'll need to figure out and create a database design that works for both you on both the computer and your iOS devices.