You can work around this issue in one of two ways, both of which are in the VirtualBox manual:
Enabling DNS proxy in NAT mode
The NAT engine by default offers the same DNS servers to the guest
that are configured on the host. In some scenarios, it can be
desirable to hide the DNS server IPs from the guest, for example when
this information can change on the host due to expiring DHCP leases.
In this case, you can tell the NAT engine to act as DNS proxy using
the following command:VBoxManage modifyvm "VM name" --natdnsproxy1 on
Using the host’s resolver as a DNS proxy in NAT mode
For resolving network names, the DHCP server of the NAT engine offers
a list of registered DNS servers of the host. If for some reason you
need to hide this DNS server list and use the host’s resolver
settings, thereby forcing the VirtualBox NAT engine to intercept DNS
requests and forward them to host’s resolver, use the following
command:VBoxManage modifyvm "VM name" --natdnshostresolver1 on
Note that this setting is similar to the DNS proxy mode, however
whereas the proxy mode just forwards DNS requests to the appropriate
servers, the resolver mode will interpret the DNS requests and use the
host’s DNS API to query the information and return it to the guest.