I have left our 21 month old twins with their grandparents twice overnight. The first time was at 15 months and it was too early, they missed us and we missed them. 2nd time, a few weeks ago was better. No way I'd do a week though.
Might have made a difference if they had been in childcare.
If you want my advice, leave it for a year or 2 until the grandparents have something constructive to offer the child.