Hi there
Yes is it possible that your LO is teething - can start at any time from birth until 18 months. In fact some LO's are born with teeth already (not wanting to offend anyone who experienced that - but boy, would that have freaked me out :lol: )
Re offering a soother - there is nothing wrong with offering a soother if you wish to, particularly if your DD has a strong sucking reflux. As the pp said though, there is a possibility that you will create a prop that needs to be weaned down the track. More likely though the extra night wakings may be as a result of a growth spurt, which are common at 6 weeks, 3 months, 6 months, 9 months (I'm not sure if there are any after that!)
You may need to offer DD some night time feeds if she is hungry, and then work on giving extra milk during the day to fill her up so she doesn't need to feed any extra at night.
HTH and good luck!