So on the birthday day - if it wasn't her birthday you would only be sending her for a few hours anyway as part of a ramp up? - a couple this week, a few more next week (birthday day) and then the following week a full or nearly full day at the FDC?

If it was me then I would just stick with that plan - and wouldn't miss the FDC as then like you say if you are leaving her for much longer the following week would be harder. She doesn't know it is her birthday - although maybe disappointing for your DH and you I would think is better for her, to go on that day and it be as normal as possible there - there will still be plenty of hours to celebrate her birthday.