Hellobee Boards

My son went through the hitting phase, but he was hitting ME. Consistency was key, but instead of saying No, we don't hit, I used language like "we keep our hands to ourselves" or "gentle touches" and then I would show him what was appropriate.

Also, redirection, because usually it was an attempt for attention and to engage me, so we'd go do a puzzle or something.

My BFF started implementing time-outs at this age. Though they were simple versions of time-outs - she'd sit with and hold her daughter for a minute (1 minute for each year old they are). Her daughter would cry the whole time during the time-out, but then they would hug and kiss and it would be over. I'm not entirely sure whether she would really learn from it or not, but now at 4 years old, she's a very polite and well behaved little girl!

We tried time outs for hitting the dog but lo didn't understand them. What ended up working with her was me getting really upset and crying about it (thank you pregnancy hormones). She is always asking if people are ok, so she saw me crying and asked if mommy was ok. I said no, mommy is not ok, I'm sad because she hit lizzie and it hurts her when she does that. Since then she rarely hits and if she does I say, lizzie is not ok because you hit her, please say you are sorry, she apologizes and stops. I think different things work for different kids, you just have to try and see what works for you.

Hitting the dog has always been an automatic time out in our house.
If LO is being generally fussy or just doing something I'd rather he not do (as opposed to breaking a hard and fast rule like "no hitting"), I'll redirect.
Counting to 3 (with a consequence like time out or revocation of a privilege or something- and we do actually follow through on this) works well if I need/want LO to stop doing something that isn't a serious infraction or isn't a discrete event (so, this might be playing with his food at the table and deliberately making a mess).
But for things like hitting, kicking, biting, etc. we immediately pick him up, tell him "We do NOT hit the dog" (we don't yell, but it's definitely in a no-nonsense strong voice) and put him in timeout. He sits in timeout by himself for a minute or two (he's currently two and a half years old) and then if he has calmed down we'll go over and talk about why he is in timeout. If he's able to articulate back to us why he's in time out and/or re-state the rule, and is ready to apologize, he leaves time out. If he gets all defiant, he stays in time out till he calms down.

I was going to say what @momof1: said. At 15 months, she really is just trying to test out some boundaries which seems defiant, but is really just curiosity. It's "fun" to see the reaction adults have! And to see if that reaction keeps happening.
I think a lot explicit talking and redirection (like "I won't let you hit. If you want to hit, you can hit a pillow - or we can play something else.") helps. Big reactions can make kids repeat the behavior.

ETA: I would have a different response if it seemed like she was hitting because she was *angry* or trying to be hurtful, but your description makes her sound more mischievous.