You can climb at 2.5 miles per hour and not fall over . I've watched ants climbing up a hill faster than I am pedaling, but have still not fallen over.

If you decide to stand while climbing, since it is a short section, do as LPH suggests and keep loose on the handlebars and keep your weight over the pedals. Then pedal as if you are dropping your leg - pushing instead of pulling. If you are seated, you again want a loose grip on the bars - I climb steep sections with my hands positioned on the tops of the bars close to the stem, and try to ensure I keep pedaling circles.

I did A LOT of climbing this past weekend, and these techniques certainly helped. You will get there - as others have said it just takes practice and training.

SheFly