Castles, I found ours via www.doula.org.uk/ just went to the appropriate geographical area, and made a list of the possible ones. Many have websites, and I got an instant feel as to who might 'fit' for us and who might not - but as it turned out, it was one of the doulas I emailed, then chatted to, who put me on to her. She couldn't do dec/jan as was starting a course - so gave me a couple of names to try instead.
No, I don't think yours sounds fishy - why not talk to her and see what your gut feeling is? I wouldn't say ours would be my best friend/confidante....but in terms of just getting the work done, and being trustworthy and professional, and getting on ok with dd (my priority) she seems great. And absolutely willing to muck in - she has three kids herself, is about the same age as me, and describes her job as being about 'supporting the family as a whole as they adjust to the new addition': just what I want!
Jabber, why not? I think doulas (both sorts) are great - and it gives you breathing space to sort out a new nanny, if thats what you plan to do, without any pressure. Its always easier making choices without pressure, IMO!
Wish I could help on the subject of diabetic cats, but... sorry, that sounds rough.