There is no way I'd hold a place for more than a couple of weeks if it was currently empty. If I was holding it, I would charge a fee for holding it, that way, if they changed their mind, the fee would be non-returnable and compensate me for wasted time.

I would also charge this fee for someone who had contracted for a place which wouldn't be available until the future - i.e. I have already contracted and filled the vacancy that will open up in September when the oldest day care child begins school. For the people who are taking that place, they have paid their two week fee to secure the opening as theirs. However, they do not require care until November so will have to pay the full rate for the place the moment it becomes empty. Because they are paying for it, they are more than welcome to have a long phase in, to come FT once the September date has passed, to return to work earlier, whatever. It's their place.
I would not be willing to hold a currently empty place until September without full-payment. As said, that's an incredible amount of lost income for a strangers peace of mind.
The most I would do for this person, is add them to a wait list and if they vacancy happens to still be available when they want it, then they've lucked in but if someone comes along needing care sooner, then the place is there for the taking.
Ridiculous that this potential client expects you not only to hold a place for such a long time but also wants the holding fee deducted from her bill when she eventually starts!