Will it be able to play Planet Zoo?
No,
the comment Luuknoord made about the dedicated graphics card is an easy way to make a first selection on which laptops will not run PZ
This game really needs good specs.
Imo, I think a laptop which could run PZ really well, is hitting the $1300-$1500 range (for a desktop slightly cheaper)
Maybe ask on this forum or on steam which players are using a laptop for PZ and ask for their specs and about the performance.
You'll get a better view on the specs.
Personally don't look at the brand name, the actual components matters more to me.
I own a HP and it runs PZ really good. There are better gaming pc's but there's a different price tag to those.