DNS shouldn't be tested with ICMP. Try dig or nslookup instead. ICMP echo request/reply may help to decide reachability and nothing more.
This is a reasonable test of the DNS service on 1.1.1.1:
$ dig @1.1.1.1 www.cloudflare.com A
; <<>> DiG 9.20.4-3ubuntu1.1-Ubuntu <<>> @1.1.1.1 www.cloudflare.com A
; (1 server found)
;; global options: +cmd
;; Got answer:
;; ->>HEADER<<- opcode: QUERY, status: NOERROR, id: 34112
;; flags: qr rd ra; QUERY: 1, ANSWER: 2, AUTHORITY: 0, ADDITIONAL: 1
;; OPT PSEUDOSECTION:
; EDNS: version: 0, flags:; udp: 1232
;; QUESTION SECTION:
;www.cloudflare.com. IN A
;; ANSWER SECTION:
www.cloudflare.com. 36 IN A 104.16.123.96
www.cloudflare.com. 36 IN A 104.16.124.96
;; Query time: 39 msec
;; SERVER: 1.1.1.1#53(1.1.1.1) (UDP)
;; WHEN: Mon Jul 14 23:32:57 BST 2025
;; MSG SIZE rcvd: 79
[EDIT]: $ ping 1.1.1.1
PING 1.1.1.1 (1.1.1.1) 56(84) bytes of data.
From 141.101.70.116 icmp_seq=1 Time to live exceeded
64 bytes from 1.1.1.1: icmp_seq=2 ttl=50 time=126 ms
So ping fails a bit (and then works - firewall) but DNS works.The service required is DNS not ping. Test the service.
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