I bought two domains and I want my users to get redirected when they try to visit www.mydomain1.com/somepath?somequery to www.mydomain2.com/somepath?somequery. Is it possible using just some service like Cloudflare and not having a dedicated hosting service per se for mydomain1.com because the sole purpose of mydomain1.com is to redirect to mydomain2.com and not to serve any webpage at all?
You can do it using Cloudflare Page Rules. Just add mydomain1.com in your Cloudflare account and create a page rule for URL forwarding with inputs as from:http://www.mydomain1.com/* to:http://www.mydomain2.com/$1