You absolutely can! We arranged ours in 7 weeks - or rather, arranged it in a week and then spent 6 weeks waiting for it to come round. A good friend arranged hers in 4, and another did it in 8! And none of us were pregnant.
You already have a church, a venue and a date, so the big points in your planning are sorted. You'll need invitations (though we did ours online), a frock, some flowers, a car, a photographer, wedding rings and to organise what you want at the reception food and drink wise. With the short time between the wedding and now it will actually be easier as you'll have to make decisions, rather than dither about all the options for ever.
I'd try to book a photographer as your next priority as in my head the photos are quite important. Also, photographers can get booked up in advance so it might be something you need to spend a little time on finding someone available. As for your dress, if you're a standard size you might be able to pick up a sample one from a wedding dress shop, or maybe hit the high street - Monsoon, Phase Eight, John Lewis, BHS and plenty of others do wedding dresses, or you could have something made. If you don't want something "weddingy" to wear then the world is your oyster.
Everything else will just fall into place - your fiance's suit, wedding rings, flowers, car are just simple phonecalls, and your invitations can be done online. It also might be worth sending a save the date to the people you want to invite via email or ring round as it's going to be a small family affair.
Good luck - and remember it's supposed to be fun! A lot of the things we are told we have to have for a wedding are just froth, you won't notice if it's not there on the day, or if the napkins don't match the bridesmaids or similar.