Just use dig. It's installed natively as part of the base system with Ubuntu (it's in the dnsutils package on Debian derived systems like Ubuntu, the package name differs on other Linux distributions), provides easy timing info for the query itself, and it's wicked fast.
Usage for your case would be something like this:
dig @1.1.1.1 one.one.one.one. ALL
The first argument (with the @) indicates what server to query (in this case, CloudFlare's public DNS server). The second argument is the domain name to search for (in this case, one of the standard names for CloudFlare's DNS service). The final one says to return all records associated with the domain (this is important if you're using a system that has both IPv4 and IPv6).
This should produce output something like this:
; <<>> DiG 9.12.2-P2 <<>> @1.1.1.1 one.one.one.one. ALL
; (1 server found)
;; global options: +cmd
;; Got answer:
;; ->>HEADER<<- opcode: QUERY, status: NOERROR, id: 4695
;; flags: qr rd ra; QUERY: 1, ANSWER: 2, AUTHORITY: 0, ADDITIONAL: 1
;; OPT PSEUDOSECTION:
; EDNS: version: 0, flags:; udp: 1452
;; QUESTION SECTION:
;one.one.one.one. IN A
;; ANSWER SECTION:
one.one.one.one. 259 IN A 1.1.1.1
one.one.one.one. 259 IN A 1.0.0.1
;; Query time: 28 msec
;; SERVER: 1.1.1.1#53(1.1.1.1)
;; WHEN: Mon Nov 12 15:09:27 EST 2018
;; MSG SIZE rcvd: 76
;; Got answer:
;; ->>HEADER<<- opcode: QUERY, status: NXDOMAIN, id: 43564
;; flags: qr rd ra ad; QUERY: 1, ANSWER: 0, AUTHORITY: 1, ADDITIONAL: 1
;; OPT PSEUDOSECTION:
; EDNS: version: 0, flags:; udp: 1452
;; QUESTION SECTION:
;ALL. IN A
;; AUTHORITY SECTION:
. 9078 IN SOA a.root-servers.net. nstld.verisign-grs.com. 2018111201 1800 900 604800 86400
;; Query time: 25 msec
;; SERVER: 1.1.1.1#53(1.1.1.1)
;; WHEN: Mon Nov 12 15:09:27 EST 2018
;; MSG SIZE rcvd: 107
The part here that you care about is the first line that says ;; Query time:, which tells you how long it took to get an answer from the moment your system sent the request until the response from the server arrived.
There's another big advantage to using dig for this type of thing. If you use a domain name that you know the IP address for, you can be certain you're getting back correct data for it. You can also test a known bogus domain (like www.bogus.bogus.), and verify that you get back an NXDOMAIN status like you should (some providers, especially ISP's, point these at advertising pages instead of saying that it doesn't point at anything).
As an alternative, why not just configure your DNS resolver on your router to query multiple servers The good ones either query all the configured servers in parallel (and as a result automatically end up using info from the fastest one, because they get the response from that one first), or they maintain info about how well each performs and preferentially query the fast ones (Unbound is an example of a server that does this).
