IDT has some pretty straightforward tools to assess the tendency of a given ssDNA sequence to form secondary structure. These tools will also predict the free energy of each secondary structure possible with your sequence.
You basically don't really need software to predict hairpin formation, but maybe only use one to see whether your sequence design yields you the hairpin structure you wish to get.
You should follow very simple rules for the hairpin design as a stem-loop design:
1. Self-complementarity - Two parts of the sequence should be oppositely complementary to form the stem part
2. Loop with no self-complementarity - The sequence in between the two stem sequences should not show self complementarity as much as possible.
3. The stability of the hairpin will be affected by the strength of the stem part (length and GC content) and by the size of the loop. A too large loop might yield also super-coiling.
4. try to avoid consecutive repetitions of the same base - this is to avoid a distribution of different interaction, aka "sliding".
5. The overall sequence size of the hairpin part should be long enough to accommodate both enough stem interactions and a loop stable enough.
Now all of the above is nice if the application requires a strong hairpin. If, on the other hand you want to use it, for instance, as a Beacon, it should be able to open up for hybridization with another ssDNA sequence (for that one can add additional sequences upstream and.or downstream to the stem edges which are complementary to part of the target ssDNA, and use the mechanism of toehold displacement. One other way is to slightly destabilize the hairpin so that when target ssDNA encounters it, it will prefer to unfold and bind it.
In summary the hairpin sequence design depends strongly also on the application for which it'll be designed.
Do you know if this is free for academic? I found this website http://eu.idtdna.com/site -is this the right one? Can you tell me which tool should I use? I have also experimental data and I know how the hairpin should look like.
You might also try Mfold program on the website of Michael Zuker. You can enter sequences and predict their secondary structure. I always use this to predict the folds of my secondary structures of RNA and DNA. It is quite straightforward.
I'm not aware of this program to be able to predict 3D structure. It also doesn't predict structural features as pseudotriloops in RNA to form. For this (since you have experimental data) I think you need a more specialized program like 3DNA or something likewise