Dear Diana,

You can transplant the pear tree now or in February.  Many transplants are done during this time period.  The weather is relatively mild.  Since you have a root growing out of the bottom, I would gently dig in the top of the soil and see how many roots there are in the pot.  Or if you can loosen the soil enough to pull the root growing outside the pot through the drainage hole. 

Lots of roots in the pot will assist if you cannot get the long root or need to cut it off.

The permanent location for the tree should be away from your home and any sidewalks.  Even dwarf trees can become a problem for foundations and sidewalks.  to make sure the roots do not come above the ground, water at the base of the tree and water deeply.

That said, to keep it small, prune judiciously, they love to grow tall.  It should also be in an area where it will get 6-8 hours of sun and have good drainage.  They don't do well in areas that flood even if it is just during the rainy season.

Dig the hole twice as wide as the pot but about the same depth as the pot.  This will give the plant the same soil level as it has had.

There are several suggestions for what to put in the new planting area.  Some say just use the soil you took out of the hole, others say put in peat or composted materials and mix with regular soil.   Adding mycorrhizae fungi  to the hole assists the roots in growing out further and brings more nutrition to the tree.  

When you take the plant out of the pot, which might be quite a task, gently shake some of the soil away and gently spread the roots out.  Make a small mound of soil in the center of the newly dug hole and spread the roots over it.  Add soil, making sure the tree is not slanting and tamp down as you layer the soil.  Water in thoroughly.

If the pot is root bound, you will need a sharp knife to slice through some of the outer roots in order for new roots to grow.

I am adding a link with detailed instructions on planting a tree, page 10 - 12.  

https://catalog.extension.oregonstate.edu/sites/catalog/files/project/pdf/ec1438.pdf

If you have further questions, please contact us again.