How to bind custom dependecy property to control's view model?

I need to create a control with few inputs / output with lots of internal functionality. I think the best approach is to create Dependency Properties for interaction with other application parts and have a private view model with hidden functions.

Here is my sample:

Window

<Window x:Class="WpfApplication1.MainWindow"
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    xmlns:app="clr-namespace:WpfApplication1">
<StackPanel>
    <DatePicker x:Name="DatePicker" />
    <app:MyControl DateCtrl="{Binding ElementName=DatePicker, Path=SelectedDate}" />
</StackPanel>
</Window>

MyControl

<UserControl x:Class="WpfApplication1.MyControl"
         xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
         xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
         xmlns:app="clr-namespace:WpfApplication1">
<UserControl.DataContext>
    <app:ViewModel />
</UserControl.DataContext>
<Grid>
        <TextBlock Text="{Binding DateVM}" />
</Grid>
</UserControl>

Control code-behind

using System;
using System.Windows;

namespace WpfApplication1
{
public partial class MyControl
{
    public MyControl()
    {
        InitializeComponent();
    }

    public static DependencyProperty DateCtrlProperty = DependencyProperty.Register("DateCtrl", typeof(DateTime), typeof(MyControl));
    public DateTime DateCtrl
    {
        get { return (DateTime) GetValue(DateCtrlProperty); }
        set { SetValue(DateCtrlProperty, value); }
    }
}
}

ViewModel

using System;
using System.ComponentModel;

namespace WpfApplication1
{
    public class ViewModel : INotifyPropertyChanged
    {
        private DateTime _dateVM;
        public DateTime DateVM
        {
            get { return _dateVM; }
            set
            {
                _dateVM = value;
                OnPropertyChanged("DateVM");
            }
        }

        public event PropertyChangedEventHandler PropertyChanged;
        protected virtual void OnPropertyChanged(string propertyName)
        {
            var handler = PropertyChanged;
            if (handler != null) handler(this, new PropertyChangedEventArgs(propertyName));
        }
    }
}

I need to achieve is to propagate date chosen in DatePicker down to MyControl's view model. Alternatively, is there any better pattern to use?