Hi Alison,
These guys dont run photo 'holidays' but they do run photo tours, so might be an option depending on how you organise your holiday
https://www.facebook.com/arcticshots/ - their website is being redone at the moment, but thats their facebook. I did their Snæfellsnes peninsula tour, which is a great area. It's photography based so can guide and give advice etc on that and do all the driving. they have a south shore trip, golden circle trip, nothern lights and i think one or two others. It's run by two guys and they are really really nice and really helpful, they even helped me out with some issues i had with my car hire the day after the day tour i did with them. I don't know what sort of group size they usually have, i only had one other person on mine, but i guess it depends what tour you do.
as
@chriscross says above, the big grayline bus tours are not the best option for northern lights if you want to concentrate on photography. i found them VERY frustrating due to dawdling people!
i guess it all depends on your budget. You could book your flight, hotel etc thru expedia or something and try and do that cheapo and then Arctic Shots (or whoever) will pick you up from your accommodation so you dont need a car if you stay in the city.
This blog is EXTREMELY good for tips
http://www.iheartreykjavik.net/ and if you search around there is a post specifically about being a lone female - though i know you've mentioned it's your first visit so that wasnt an ideal scenario for you, but just so you know its out there. She runs a great walking tour, which is ideal to do on your first day to get to know the city and also, as they are popular, you could meet new people on that.
There's also an area walking distance (technically) just outside of the city that is dark enough to take NL photos if they showed up. just the backdrop isnt as great as it could be, but the lights are still pretty!!
Don't know if thats much use and know there are lots of others Iceland-philes on here that may have other suggestions. I'm looking to go back in September for a couple of days but hoping to head over East on a whirlwind trip, as long as all the accomodation in Vik doesnt sell out!!
D