I am not from the Ukraine, but wanted to say Hi : )
I came to Canada from the states as a Married person. While we didn't have "trouble," we did have a lot of paper work to do and months of waiting until it was all finalized.
You need to look at the site below, if you haven't already done so.
Do you and your BF have one of the skills on the list? If you do then you should start seeking employment and get the requisite valid offer of arranged employment. Cross your fingers and hope that the position is still available when your application is processed.
If you work in the medical field, it looks like you are golden. If you speak French or one of the major languages of India that is a bonus in the GTA.
Take time to decide where you want to live and know that each province is as different as each state. For instance in BC there is a heavy Asian population and in New Brunswick being Bilingual is a must for some fields...but not very important in Nova Scotia. I have been in NB for 4 years and have had a hard time finding work because I am not bilingual...though I do have a Master's Degree.
Additionally keep in mind that you may be accepted and your BF may not. Though one of you could apply later as a common law spouse if you are currently living together and can prove your relationship is "real." I scanned the application and you may be able to apply together if you are truly common law.
The fees are non-refundable if you are refused, keep that in mind. The total fees for my application and PR Card went well into the $600 range.
As for staying for six months, that is for a visitor. You can't work here for six months or receive any benefits...unless you do it illegally.
One question, when did your father come to the USA? Things might be a lot different today. My friend was married for two years and had a baby before her husband became a permanent resident of the USA. That was in 2007, the wheels of immigration move slowly in both countries.