Assuming the real life Pegasus Dwarf Irregular Galaxy is the same one as in Stargate it is 3.001 million light years away from Earth. Based on http://stargate.wikia.com/wiki/Pegasus they sound the same just going on the dwarf description and distance.

The Prometheus Class tops out at a Warp factor of 9.975. That can cover a distance of 132 light years in 1 month, 40 light years in five days, 70,000 light years in 70 years. (Source: http://memory-alpha.wikia.com/wiki/Warp_factor#Warp_factor_vs._average_speed)
The math:
132 light years / 1 month (30 days) = 4.4 light years per day
40 light years / 5 days = 8 light years per day
70,000 light years / 70 years (25,550 days) = 2.739726027 light years per day
Since that gives such wildly different values I will take an average of 5.046575342 light years per day.

3.001 million light years at 5.046575342 light years per day = 15144772.6 days or 41,492.52768 years.

BC-304 class ships without a ZPM can travel from Earth to Atlantis in 18 days days. (Source: http://stargate.wikia.com/wiki/BC-304#Hyperdrive)

So Star Trek ships are fucking slow compared to Stargate ships. That doesn't seem right at all. The Prometheus of the Prometheus Class ships was launched in the 2373.

The Daedalus of BC-304s was launched in 2005.

https://www.youtube.com/watch?v=llMgzC3qHXw

Fastest to slowest
Halo (Forerunners)
Stargate
Star Wars
Halo (humans)
Star Trek

Fucking Star Trek their engines suck.