Mini Split liquid line shaking
I just had a training class that mentioned these units a few weeks back (even offered a bounty to get more views). The system comes fully charged you just assemble it and connect the lines. All hvac systems vibrate and this is normal. I hope you reviewed the instructions and the feed back to seal the threads on the line set. I use nylog (nylog blue for the last few years). Movement is somewhat normal especially with the 25’ line set so having the thread sealant is a good idea and will reduce the number 1 cause of failures low refrigerant (this was what the instructor told us). 
Yes some vibration is normal the pad you mount the unit helps dampen this,  so I would not worry two much about that. 

With dogs (I love dogs and have them) make sure they do not pee on the outside unit. Dog pee is very corrosive and will wipe out the outside coil much faster, I have seen this several times on systems where dog pee ate the fins and eventually caused holes in the tubes.  But as far as some vibrations of the pipes this is normal.