In my neck of the woods, I don't see much in the way of fruit from a new tree for the first three to five years. So, were I you, I wouldn't count on much fruit for a while. Trees are a long term investment.
To answer your question, I agree with Greg above. In a word- no.
Perhaps you've heard the old saying that you "plant pears for your heirs". Pear trees are often slow to do much following the first few years after planting. Thereafter their pace picks up. A wise old orchardist once described the growth pattern of a pear tree to me as "sleep, creep, leap". Without knowing the exact dwarf rootstock your pear is on, it's still safe to say that your tree will fruit sooner that if it was on standard rootstock. Dwarf rootstock trees won't live as long as standard rootstock trees but you probably don't care if your pear tree is still alive in 150 or 200 years!
Your picture shows leaf buds. Once your tree starts to spur or form fruit buds you'll know you're getting close.
Leaf bud on the left, fruit bud or spur on the right:
"There are some who can live without wild things, and some who cannot." -Aldo Leopold
Fiera Sprite wrote:Thanks so much for all of your help! The picture is incredibly useful.
I am new to all of this. My fruit bushes and dwarf cherry tree all produced on the first year so I had just assumed that the pears would too. I am glad I know what to expect now.
In general, prunus (plum/cherry/peach) produce fruit much faster than pears. For some perspective, back in 2009 I planted a wide range of fruit trees from a commercial nursery. Fast forward a decade, and the peach trees were all dying of old age while the pear trees were finally just starting to produce a decent crop.