First, understand that the hitting is very normal. Even if they aren't exposed to hitting, sometimes kids do it. 1.5 years is hard because you know they understand a lot, but the problem is they don't have self control. That develops closer to 3. So what do you do? At that age, I had a few strategies.
1. Redirection. She goes to hit you playfully and you catch her and say, "Alright! Give me a high 5!"
2. Distraction. She playfully hits and you ignore it and ask her to get a book or her blocks or sing a song for you.
3. Tell her what she can do. "Hitting hurts, we don't hit. If you're mad, hit a pillow/stomp your feet/clap your hands/say Mommy, I'm mad!/etc."
4. Gently remind her "Hands are not for hitting, they are for giving high fives/for petting the cat/for playing patty cake/etc. There is a book on Amazon called Hands Are Not For Hitting and it tells you what hands are for. Maybe reading this everyday will reinforce things.
5. If she hits you, I think it is ok to tell her, "I do not like to be hit. Hitting hurts, I like hugs and kisses better." If you get a hug or kiss make a big deal about it. If she keeps hitting, repeat, "I do not like to be hit." and walk away for a couple minutes.
All or some of these might help you. I'm not big on time out, especially at that age, so I didn't suggest it. There are so many other things you can do to teach your child to behave other than plopping them in their crib or highchair for 1.5 minutes and listening to them cry for doing an age appropriate behavior. I didn't use time out until my daughter was well over 2.5 and then, very sparingly. That's just my preference. I know you'll get that as a suggestion from other moms though.
Good luck! Just say consistent in addressing the issue and this phase will pass. =)