Over the last decade, Web traffic has significantly shifted towards HTTPS due to an increased awareness for privacy. However, DNS traffic is still largely unencrypted, which allows user profiles to be derived from plaintext DNS queries. While DNS over TLS (DoT) and DNS over HTTPS (DoH) address this problem by leveraging transport encryption for DNS, both protocols are constrained by the underlying transport (TCP) and encryption (TLS) protocols, requiring multiple round-trips to establish a secure connection. In contrast, QUIC combines the transport and cryptographic handshake into a single round-trip, which allows the recently standardized DNS over QUIC (DoQ) to provide DNS privacy with minimal latency. In the first study of its kind, we perform distributed DoQ measurements across multiple vantage points to evaluate the impact of DoQ on Web performance. We find that DoQ excels over DoH, leading to significant improvements with up to 10% faster loads for simple webpages. With increasing complexity of webpages, DoQ even catches up to DNS over UDP (DoUDP) as the cost of encryption amortizes: With DoQ being only ~2% slower than DoUDP, encrypted DNS becomes much more appealing for the Web.