The longer-term solution is to wait for DoT to become prevalent in authorative servers.
But, realistically, won’t you “leak” your IP anyway when you make your actual connection? I mean, why are you looking up things in the DNS if not to connect to them? And if you make a connection, you leak your IP.
If you’re not concerned with the other party’s DNS servers, but with the root servers and TLD DNS servers snooping on your queries, I think you’ll have to wait for QNAME minimization to arrive.