I've heard that the chances of getting pet by 99 is around 50%.
Do 2 full magic tree runs, 1 palm tree run, calquat tree, hespori, 3-5 herbs, and 3-5 snape grass (allotment) runs daily.
Getting the pet is all based on that specific harvest item's base chance. Higher tiered farming tiered items, therefore, provide better base chances.
I.E. at level 98 you have a 1/6,918 chance of pet from a magic tree harvest, whereas at level 98 you have a 1/171,527 chance for each snape grass you harvest.
Your best bet is to do several different types of patches (this is why the above mentioned daily run works great).
I've heard that planting seaweed is also a great way to get pet.
The rate at 98 farming for Tangleroot thru seaweed is 1/4550. That makes it better odds that with trees.. and you can farm multiple seaweed per plant. Whereas trees is 1 shot per tree.
Good luck.