Aikorob,
I can understand her nervousness and hope everything goes off smoothly.
There are several options to choose from but a few I can think of are listed below:
1. Jack from this board has a contact in Kiev who has a private car and will do an airport transfer for "N". I'm sure you can PM Jack and he will put you in touch with him.
2. Have a look at this website in the transportation section of this page:
http://www.translations.kiev.ua/index.php?mode=price&lang=enThey can organise a private car with driver for $35 but if you want her to feel a little special why not organise a Luxury Car for $50. You could arrange for the driver to leave a single red rose on the back seat as a surprise when he collects her from the train station.

OK OK... I'm just missing my girl so I'm getting a bit mushy.
This site looks like a good option though because they post all their prices right up there for us to see.
3. No doubt El Rock will promote his girlfriend though I don't know if she has a car. You might PM him to pre-empt his marketing pitch.

4. Some in here will recommend Pavel. If you choose to use Pavel be very clear that all you need is a private car with driver and you won't need his services at the same time. If you use a guide + a car you'll effectively pay double the price.
5. There's aways plenty of taxi's outside of the train station in Kiev and I'm sure she'll still be able to get one even if there is "trouble". It might be nice to get a private car though because the driver should meet her at the platform and help her carry her bags.
6. If you want something more personal my best friends in-laws are in Kiev and he has offered his FIL's car (or his Brother in law) when I am next in town. They're nice people (I've met them a few times) and if they are available I'm sure they'll be happy to help. (They'd probably be excited to help because they're currently waiting for their immigration application to be approved before they move to Aus permanently.)
No matter which way you get her to the airport it should cost no more than the $35 on the website I posted above. From memory my taxi from the centre of Kiev to the airport as 150 grivina and the train station to the centre is 25 grivina.
Hope this helps.
Kuna