I am a nail technichian and wish I lived closer to you! The bad news is it will take 12 - 18 months to grow a new one...darn. Good news is go to a good reputable nail salon or spa and ask for them to make you a new toenail! It can be done with acrylic. Just make sure to keep it clean and dry and if you notice any lifting to get in and get it repaired asap to avoid getting fungus in it. I have been doing french pedicures with gels and it is holding up great, so I would imagine that gel or acrylic would work great on your big toe!
Had an extra thought as I was reading thru the responses. If you are embarassed about it don't fret cuz I have seen some gnarly, nasty, smelly feet in my day...a missing toenail is kind of fun for a nail tech, makes us feel like we really are helping! Also, if you are low on cash...go to a cosmetology school for a pedicure and have this service added on. Just make sure to ask for a nail student, not a hair, makeup and nail student! Nails only!