Can you pay for a subscription for just one month?

we wouldn't need it for a whole year

Sure, you can upgrade your account to a paid plan for a month. In the pricing page choose the plan you want to subscribe and hit the upgrade button. After that you will be able to choose the monthly payment schedule. Please see the pricing page : Pricing

Note that you need to downgrade your account to the free plan since JotForm auto-renews at the end of each term. For further information please take a look at our Terms of Use