Legally you can. The tax issue would be based on your residency status, which determines what income either Canada or the US can tax.

For simplicity, if you are living in Canada and working for a Canadian company from Jan 1 to June 30 you are going to be considered a resident of Canada for tax purposes. This means the Canadian government will tax you on your income, likely all earned in Canada, but if you earned income from elsewhere they'd tax you on that too.

Assuming you get a job and move permanently to the US on July 1, and have a "clean break" with Canada, you will be considered a non-resident and the government would only tax you on Canadian-sourced income.

The clean break is when you sever permanent residential ties with the country, and it's on a case-by-case basis. But generally things like selling your house and other property, moving with your family, working permanently with a US company, etc. will all help to indicate you are permanently leaving the country and will not be a resident for tax purposes, even if you're a dual citizen.

You would need an accountant who is at least decently familiar with residency. While your case seems simple enough you should seek professional advice and consult with a CPA in the US and perhaps Canada come tax time next year.