Considering 9.1.x isn't supported anymore, it would be a good idea to upgrade. I've been suggesting to our customers to wait to upgrade production units to 10.x until 10.0.2 at the earliest. So 9.4.8 would be a good choice for a production environment.
You'll need to upgrade to 9.2 first and then to 9.4.x:
https://support.f5.com/kb/en-us/products/big-ip_ltm/releasenotes/product/relnotes_9_4_8_ltm.html
Warning: Version 9.0.x or 9.1.x installation. You cannot upgrade directly to this version from BIG-IP versions 9.0.x through 9.1.x. You must first upgrade to version 9.2.x, or an earlier version of 9.3.x or 9.4.x. For details about these installation methods, see the release notes for the associated release.
Your configuration should be upgraded automatically. You may want to review the final 9.4.8 configuration to optimize it using new features in 9.4.8 that didn't exist in 9.1.x, like the LAN optimized TCP profile, etc.
Aaron