Does she understand No or Quiet. If not practice these two commands at home, especially No. Its a very useful command for all sorts of outside walks. I presume she's barking at everything because shes a bit scared of them and trying to be brave.
Take her back to the park at a quiet time if you can. If she starts to bark, just say No firmly but calmly. Then try and distract her excitedly by taking her off in the opposite direction. Use exciting commands, like This Way, Whats This, etc
I think you'll find the barking will decrease as she gets more used going outside, so try not to do less of it,
Is the park fairly secure or particular big. You might like to try her off lead. If she has a tendancy to follow you around at home she is very likely to want to stay close to you outside in the park too. You may find she is better off lead. Its a good idea to get her off lead as early as possible as while she is lacking confidence she shouldn't run away and will learn to keep you in sight.
A couple of things to bear in mind. Take some high value treats, ie sausage, frankfurters, chicken, cheese. Whilst still on the lead do a couple of simple commands ie heel, sit, wait and reward. That way she knows you have nice tasty treats with you, Then let her off the lead, she should just explore gently, taking in all the new smells. Keep walking and encourage her to follow with This Way. Stop and recall her with Come or Here or whatever you use. You must be very exciting and enthusiatic. Lots of praise when she returns and touch her collar then reward. As time goes in, put her lead back on for a little while and take it off again, she needs to understand that the lead can go back on at any time, not just to signal the end of the walk.
Once your confident she is keeping with you, practice a game of hide and seek, really easy versions. Hide, stick your head out and call. Praise and Reward. Gradually Hide and call. The idea of this is to train her to keep and eye out for you at all times, not just you watching her.
Even now, when Millie is off lead, she may be confident and can wander off, she will always keep us in sight.
Good luck and don't be put off with the barking and lunging it will pass. By the way where are you based, you may be able to meet up with another cockapoo owner on here to give your cockapoo some confidence,
