You can contact the province of Canada which you may want to move to see if their Ministry of Transportation (or their agency that is comparable to a State's department of motor vehicles) to see if you can obtain a licence there while having a suspended license in the US.
For example the Ministry of Transportation for Ontmario states that all applicants that want to exchange an out of country driver's license for an Ontario driver's licence are required to present a valid foreign driver's licence. If you can obtain an Ontario driver's license without exchanging or notifying them of the suspended license (thus not valid) is something the MTO would have to answer for you.
The Alberta Government notes for exchanging a non-Alberta license that a valid licence from the United States can be exchanged for a Class 5, 6, or 7 when the applicant is presenting a valid licence of equivalent class. Once again the US license must be valid.
Since to exchange a US license for a Canadian licence it appears your US license would need to be valid, it might be that you can acquire a license but would have to start the whole process as if you were unlicensed or a novice driver. Or the province may require that you wait until your US license is reinstated before they will permit you to obtain a Canadian license.
So it may be possible to acquire a Canadian driver's license if you have moved there while having a suspended US license but you will need to check with the licensing authorities of the Canadian province.
For a Canadian car insurance quote follow this link.