This type of tool is extremely effective for dandelions. If you go out and do a few every time you take her out, they'll be under control in no time at all.
When I'm killing them in a driveway or patio, I usually just boil up a big pot of water and go around dumping it on them. They shrivel up on contact. It also cooks any seeds stuck between patio bricks so you don't get new ones right away.
It'll kill your grass though, so won't work on a lawn unless you can target it
exactly onto the dandelion. Even then, I don't know if you can get it down to the root without it killing nearby grass roots.
ETA: if your lawn has large solid clumps and patches of weeds though, the boiling water would work really well for that.