Laura-

 Before I can provide some guidance, I need to understand
your status a bit better.

I gather you are job searching and perhaps you are in
treatment or recovering from treatment. 
Is this correct?   What timeline
has your doctor given for when you could return to work?

 Do you have interviews scheduled at this time? Generally,
you are not asked about a firm start date at time of interview, and if asked ,
you can be vague.  Start dates are
negotiated when an offer is tendered. 
All they are looking for at the interview stage is some indication.  This is similar to the question:  what are your compensation expectations?

 If the application
form requires that you give a start date, you can put down TBD (to be
determined) at time of offer.   If you
are asked verbally, tell them that it depends when an offer may be tendered;
you can indicate that you have a project that you are currently working on.  The timeline between an interview and an offer
can sometimes be as long as 4-6 weeks depending on the type of position.  If you are asked when your project end, use
the date the doctor gave as your possible return to work date.

 Hope this is helpful. 
I can provide further guidance once I know your current status.

 Margot