Insofar as your iPad is capable, its system software is up to date. The first generation iPad Air, iPad mini2 and mini3 can only be updated to iOS 12.5.5.
Apple ended major update support for these models of iPad in September 2019 - although they continued to receive occasional “point” security updates until late last year. These devices cannot be updated to iPadOS 13 (or any later major versions of iPadOS) as the internal hardware does not meet the minimum technical requirements (CPU capabilities and available RAM) for newer versions of iOS/iPadOS.
It is unclear as to whether or not earlier (now unsupported) versions of iOS are exposed to the same Kernel and WebKit vulnerabilities that the iOS/iPadOS 15.6.1 security update is explicitly intended to address.
Regardless of explicit exposure, your iPad is now unsupported. For older devices, no longer benefiting from regular security updates, the risk of an unpatched vulnerability being exploited increases.
A useful measure by which you can reduce potential exposure to exploits (applicable to all computers), is to use a security focussed DNS Service in preference to automatic DNS settings. This can either be set on a per-device basis in Settings, or can be set-up on your home Router - and in so doing extends the benefit of this specific protection to other devices on your local network. I suggest using one of the following DNS services - for which IPv4 and IPv6 server addresses are listed (you should configure all four addresses for the chosen service):
Quad9 (recommended)
9.9.9.9
149.112.112.112
2620:fe::fe
2620:fe::9
OpenDNS
208.67.222.222
208.67.220.220
2620:0:ccc::2
2620:0:ccd::2
Cloudflare+APNIC
1.1.1.1
1.0.0.1
2606:4700:4700::1111
2606:4700:4700::1001
Use of the above DNS services will help to shield you from “known bad” websites and URLs.
There are advanced techniques to further “harden” iOS/iPadOS (such as using DoH, DoT and DNSSEC) - but these may be beyond the reach of less experienced users.
