You might want to aim for shifting your voice to falsetto when you laugh. It seems like my body naturally shifts my voice higher in order to facilitate laughing. That works especially well for heavy laughter, which if you think about it is really just screaming in short, random bursts. It also seems that the faster you expel the air from your lungs, the higher the sound you can produce.
This video features two men laughing, but they get pretty high pitched. Try to listen to the son's laugh just because the father tends to get a couple bass-riddled heaves in his laugh.
I wouldn't say mimic them exactly, but that's probably the effect you want to go for a big, all out laugh.
Having a little bass sound in your laugh is okay, though. In the video below, the woman on the right has a deeper voice, and her laughter is occasionally punctuated with deeper sounding "huhs" and such.
Contagious laughterThis woman goes high and deep with her laughter:
best laugh attack ever!So, I think you have to find balance between falsetto and chest voice, just like with speaking in a feminine voice. The issue with laughing is that you lose voluntary control over some of your muscles, so you have to consciously keep your voice box in the female voice position. It might help to practice laughing, as dumb as that may sound. Like, watch a video that always makes you laugh and just consciously prepare your voice for laughing. I think, like the voice, it's one of those things that just becomes natural after practice.
Hope that helps or maybe gives you something to try out!