doq: configure QUIC keep-alive and retry on idle timeout

Pass a quic.Config with KeepAlivePeriod (15s) to DoQ dial calls instead
of nil, so pooled connections send periodic QUIC PINGs to stay alive and
detect dead paths proactively.

Also add IdleTimeoutError to the DoQ retry conditions alongside io.EOF,
so stale pooled connections trigger a transparent retry instead of
propagating as a query failure.

doq.go

@@ -46,6 +46,7 @@ type doqConnPool struct {
 	addrs      []string
 	port       string
 	tlsConfig  *tls.Config
+	quicConfig *quic.Config
 	conns      chan *doqConn
 }
 
@@ -65,11 +66,16 @@ func newDOQConnPool(uc *UpstreamConfig, addrs []string) *doqConnPool {
 		ServerName: uc.Domain,
 	}
 
+	quicConfig := &quic.Config{
+		KeepAlivePeriod: 15 * time.Second,
+	}
+
 	pool := &doqConnPool{
 		uc:         uc,
 		addrs:      addrs,
 		port:       port,
 		tlsConfig:  tlsConfig,
+		quicConfig: quicConfig,
 		conns:      make(chan *doqConn, doqPoolSize),
 	}
 
@@ -85,12 +91,17 @@ func newDOQConnPool(uc *UpstreamConfig, addrs []string) *doqConnPool {
 
 // Resolve performs a DNS query using a pooled QUIC connection.
 func (p *doqConnPool) Resolve(ctx context.Context, msg *dns.Msg) (*dns.Msg, error) {
-	// Retry logic for io.EOF errors (as per original implementation)
+	// Retry logic for transient errors: io.EOF (connection reset) and
+	// IdleTimeoutError (stale pooled connection timed out).
 	for range 5 {
 		answer, err := p.doResolve(ctx, msg)
 		if err == io.EOF {
 			continue
 		}
+		var idleErr *quic.IdleTimeoutError
+		if errors.As(err, &idleErr) {
+			continue
+		}
 		if err != nil {
 			return nil, wrapCertificateVerificationError(err)
 		}
@@ -226,7 +237,7 @@ func (p *doqConnPool) dialConn(ctx context.Context) (string, *quic.Conn, error)
 			udpConn.Close()
 			return "", nil, err
 		}
-		conn, err := quic.DialEarly(ctx, udpConn, remoteAddr, p.tlsConfig, nil)
+		conn, err := quic.DialEarly(ctx, udpConn, remoteAddr, p.tlsConfig, p.quicConfig)
 		if err != nil {
 			udpConn.Close()
 			return "", nil, err
@@ -241,7 +252,7 @@ func (p *doqConnPool) dialConn(ctx context.Context) (string, *quic.Conn, error)
 	}
 
 	pd := &quicParallelDialer{}
-	conn, err := pd.Dial(ctx, dialAddrs, p.tlsConfig, nil)
+	conn, err := pd.Dial(ctx, dialAddrs, p.tlsConfig, p.quicConfig)
 	if err != nil {
 		return "", nil, err
 	}