Well, like other Pokemon (Looking at you, Kriketune), most early Pokemon lose their usefulness after a certain point. Unless we get M-Lopunny soon, which we won't, you may want to find another option.
You could always trade the Growlithe you receive for an Azurill, but since you lack a good fire type, you could go back to the city and get yourself a Numel on a rainy day.
If you do decide to grab the Azurill, it wouldn't be a shabby idea as Ame will probably remove said trade as Azumarill is INCREDIBLY strong at the early levels, with a 90 base STAB move @ level 25.
EDIT: Yes! Bunnelby (Diggersby) Would be a great alternative! Make sure to pick up one with Huge Power.