We cut my daughter's hair when she was 1 year old... she loved it! We took her to a "kiddie" place to cut her hair. They know how to handle little kids.
If not, and you do it yourself, you will probably need 2 people... one to hold her in his/her lap, and you cut say the bangs. That is also what we did when my daughter was little... and for my son who is now 3 years old and HATES to cut his hair.
The main thing is to distract them with something... even if in front of a tv. Which is what the Kiddie salon does, where we went. And, watch their hand/arms... because they may try to swat you or yank away... or flail their arms.
If not, then you just try to make due... and not cut her hair until you feel comfortable with it, and she.
If she pulls her hair clips out, then just don't use it. She will probably yank them out at daycare too....and then it can become a choking hazard for her or other little kids/babies who are around. Many kids yank out their hair accessories... So... you can just let her hair grow, which is what many Moms do too. Until they get to an age where cutting hair is not so difficult.
Or sometimes what we do, with our son, is we cut his hair while he is in the tub. Note: I said "WE cut his hair" ... meaning I do not do it by myself... my Hubby helps me. He is in the tub holding our son, and I am on the sidelines of the tub, cutting. And then we shower off.
All the best,
Susan