Hi Minnu ,
Advanced Bday wishes to the little one .

In my opinion , visiting neighbours with gifts could be avoided , it may put them in a rather uncomfortable spot . They may also feel compelled to give something in return .
From my experience , kids don't mind not having a party when they are two .It may matter when they are three but not at two.
If you really want to do something ,you could have a snack party in the late afternoon just for the moms and kids in the neighborhood.Cake,chips,drinks and something like samosa should be enough .You can distribute return gifts then .But you need to keep it short , maximum for 90 mts or so.Plan around the child's naptime.
Else just take her out to her favorite place and keep it a simple family affair .They will love a party when they are three ,you can have a gala party then.
Good Luck
Shobana