Honestly, you could start her in agility, just for fun! There are Beagles that go into this sport and i'm sure they are WAY more stubborn then your girl lol
The jumps are lowered considerable for smaller dogs. you'd be surprised the breeds of dogs that enjoy this sport. I've see Chiuauas(sp?) at shows(my mom co-owns an agility club), i've seen min pins, beagles, viszlas, dalmations.. breeds you would really expect to do agility, but they all just LOVE it!
I do suggest getting her out for walks more though, having an overweight dach can lead to back problems for them because of their elongated bodies. Your girl may just happen to enjoy agility though. just take it easy for sure.
Also, the agility you see on tv is for advanced fully trained dogs, that is why they have sharp turns and such in it.